IB Physics HL A.1 Kinematics Questions

SLSL HLHL

Practise IB Physics HL A.1 by solving motion, projectile and drag problems with position, velocity and acceleration data.

190 questions in this syllabus scope, with question parts counted together.

Exam points & syllabus

Exam points

Use graph axes and signs to distinguish speed from velocity, and displacement from distance travelled.
Relate a displacement or height graph’s slope to velocity and its changing slope to acceleration when interpreting or sketching motion.
Estimate an instantaneous rate with a tangent at the stated point; distinguish it from an interval average.
Use signed graph areas for changes in motion: velocity–time gives displacement and acceleration–time gives velocity change.
For nonuniform motion, estimate area using an appropriate geometric approximation and account for the portion that the curve omits.
Calculate average speed from total distance and average velocity from net displacement, dividing by the same complete time interval.
A turning point can have zero velocity and nonzero acceleration; constant speed on a curved path also involves velocity change.
For a rebound, use the signed velocity reversal and state the acceleration’s direction; identify which interval the question requests.
Apply SUVAT only within a constant-acceleration stage, keeping initial conditions, signs and units consistent.
Use squared-time or square-root-distance scaling for motion from rest, and distinguish successive interval distances from cumulative displacement.
Solve catch-up or equal-position events by comparing both positions at the same time; discard an initial meeting when a later one is requested.
Retain the ground-frame initial velocity of an object released from a moving balloon and select the later physical root.
Use same-height ascent/descent symmetry or the return-time condition to determine launch speed or an intermediate height.
Link the speed and duration of each journey stage before applying the full speed–time area or total-distance condition.
In an oscillation-trace experiment, use the complete cycle count and calibrated distance, then report acceleration with a consistent unit.
Resolve launch velocity using the angle’s actual horizontal or vertical reference and preserve upward or downward launch signs.
For ideal projectiles, keep horizontal velocity constant and vertical acceleration downward; draw each component graph from its own initial value.
Use horizontal travel to find one shared flight time, then test the vertical height or clearance at the wall or net.
Include release height when comparing maximum rise with a ceiling or converting vertical displacement into height above ground.
For horizontal launch, find fall time from height before range; for an oblique cliff launch include its initial vertical component too.
Separate speed from velocity components at equal-height return: vertical direction reverses, and equal launch energy fixes impact speed.
Recover total initial speed from measured horizontal distance, time and launch angle; a horizontal component is not the full speed.
Draw a velocity vector tangent to the path from the specified point, and an ideal free-flight acceleration vector vertically downward.
Explain changing acceleration through a force that varies with speed or position, rather than applying one constant value throughout.
For escape above the required speed, describe decreasing speed and decreasing deceleration with a nonzero limiting velocity.
With drag, combine weight with velocity-opposing resistance; vertical acceleration differs on ascent and descent and horizontal velocity can decrease.
Explain terminal motion through drag balancing weight: acceleration and resultant force approach zero while speed stays nonzero.
Distinguish the graph of decreasing resultant force from increasing drag, and relate the displacement slope to terminal speed.
Use a supplied drag law with terminal balance, or a transient tangent and Newton’s second law, to determine its coefficient.
For the given air-to-water entry model, sketch speed falling to a lower nonzero plateau and stop the graph before bottom contact.
Support a given approximate result with correct substitution or sufficient precision; an unsupported rounded target may lose a method mark.
In the stated raindrop-in-air model, initial drag is zero and acceleration is approximately g; resistance then builds as speed increases.

Covered syllabus points

A.1.1—Position, velocity and acceleration A.1.2—Velocity and acceleration rates A.1.3—Displacement A.1.4—Distance and displacement A.1.5—Instantaneous and average values A.1.6—Uniform acceleration equations A.1.7—Uniform vs non-uniform acceleration A.1.8—Projectile components A.1.9—Fluid resistance on projectiles

Exam points

For a vertical throw, speed falls to zero at the apex and rises on descent; keep the speed graph nonnegative.
Use a displacement graph’s gradient to describe velocity: a straight segment means constant velocity and a decreasing positive slope means slowing forward.
For an initially stationary raindrop in the stated air-resistance model, give the initial acceleration as approximately g, with its unit.
Locate greatest rebound height at the post-bounce zero of velocity, rather than the initial release or contact interval.
Sketch rebound height as a concave-down curve with positive initial slope and zero slope at greatest height.
Use the full distance travelled in a speed calculation: clearing a field region requires its length plus the loop’s width.
Draw instantaneous velocity tangent to the trajectory, starting at the specified point and pointing along the motion.

[Maximum number: 1]

A student throws a ball towards a wall. The ball is released from a point 1.8 m above the ground and 8.0 m from the wall. The initial velocity of the ball makes an angle of $48^{\circ}$ with the horizontal. Air resistance is negligible.

The diagram shows the initial path of the ball. P is a point on the path.

Draw, on the diagram, an arrow to show

the velocity of the ball at P . Label this arrow v.

Exam points

Use the gradient of a velocity–time graph for acceleration; a nonzero slope can persist while velocity passes through zero.
Use the signed area under acceleration–time to find velocity change; the graph alone does not give displacement or absolute velocity.
Calculate average acceleration as signed velocity change divided by elapsed time, converting speed units first.
At a vertical turning point, zero velocity does not mean zero acceleration; gravity still acts when air resistance is negligible.
Estimate instantaneous acceleration with a tangent at the stated time and show the gradient calculation when it earns a separate mark.
Constant speed on a curved path still gives acceleration because the direction, and therefore the velocity vector, changes.
When sketching velocity from acceleration, match its slope to the acceleration pulse; the acceleration does not set the initial velocity.
For a rebound, account for the velocity reversal in Δv and state the acceleration’s direction relative to the incoming motion.

[Maximum number: 2]

A toy rocket is made from a plastic bottle that contains some water.

Air is pumped into the vertical bottle until the pressure inside forces water and air out of the bottle. The bottle then travels vertically upwards.

The air-water mixture is called the propellant.
The variation with time of the vertical velocity of the bottle is shown.

The bottle reaches its highest point at time $T_{1}$ on the graph and returns to the ground at time $T_{2}$ . The bottle then bounces. The motion of the bottle after the bounce is shown as a dashed line.

Estimate the acceleration of the bottle when it is at its maximum height.

Attempt to calculate gradient of line at $t=1.2 \mathrm{~s}$

«-» 9.8 «m s ${ }^{-2}$ » (accept 9.6-10.0)

Exam points

Find displacement from the signed area under a velocity–time graph, using the actual axis scales.
Combine perpendicular displacement components by Pythagoras for the magnitude; adding them gives a different quantity.
Interpret negative displacement using the stated origin and positive direction; a negative sign does not mean a negative distance.

[Maximum number: 1]

This question is in two parts. Part 1 is about kinematics and gravitation. Part 2 is about radioactivity.

Part 1 Kinematics and gravitation

A ball is released near the surface of the Moon at time t=0. The point of release is on a straight line between the centre of Earth and the centre of the Moon. The graph below shows the variation with time t of the displacement s of the ball from the point of release.

State the significance of the negative values of s.

Exam points

Calculate average speed as total distance divided by total time, counting every leg even when direction changes.
Calculate average velocity from endpoint displacement over elapsed time; a reversal can make it differ from average speed.
Distinguish an interval average from the speed at one particular instant; the definitions need both time scopes.
Estimate instantaneous velocity from the displacement–time tangent at the requested instant, preserving its sign or stating its direction.
If acceleration rises linearly from zero and initial speed is zero, sketch speed increasing from the origin with an increasing gradient.

[Maximum number: 3]

This question is in two parts. Part 1 is about kinematics and gravitation. Part 2 is about radioactivity.

Part 1 Kinematics and gravitation

Use the graph to

estimate the velocity of the ball at $t=0.80 \mathrm{~s}$ .

tangent drawn to curve at 0.80 s ;
correct calculation of gradient of tangent drawn;
$-1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ or $1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ downwards;
or
correct coordinates used from the graph;
substitution into a correct equation;
$-1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ or $1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ downwards;

Exam points

Treat SUVAT as a model for uniform acceleration; its empirical basis does not make it valid for arbitrary changing acceleration.
For motion from rest at fixed acceleration, distance scales with time squared and speed scales with the square root of distance.
Find distance during uniform acceleration from the mean of initial and final velocities multiplied by the interval time.
Use v² = u² + 2as when time is absent, preserving the deceleration sign for a stopping-distance calculation.
Distinguish distance travelled in each successive second from total displacement since release.
For two objects with the same gravitational acceleration, compare their positions at the same time; common quadratic terms can cancel.
Set the two travelled distances equal for a catch-up event and reject the trivial initial meeting at t = 0.
Use the appropriate constant acceleration for each stage or setup; an earlier Moon value does not replace Earth’s g.
For free fall from rest, connect the given drop height or fall time to the impact speed; horizontal launch speed does not set fall time.
Use equal-height ascent and descent times symmetrically to locate the apex and recover initial upward speed.
Use the return-time condition to express launch speed in terms of the total flight time before finding an intermediate height.
For an object released from a rising balloon, retain its upward ground-frame initial velocity and select the later positive impact time.
Link a stage’s duration to its final speed before using the full speed–time area for a journey with different acceleration stages.
Define the time interval carefully: a post-contact travel time excludes an earlier pushing interval.
Show numerical substitution or sufficient extra significant figures when establishing a given approximate value.
Use the complete oscillation trace to find travel time and distance before applying s = ½at²; report the acceleration with a consistent unit.
For a released alpha particle between uniform plates, use the full plate gap and its constant acceleration to determine crossing time.

[Maximum number: 4]

This question is in two parts. Part 1 is about kinematics and gravitation. Part 2 is about radioactivity.

Part 1 Kinematics and gravitation

(a)

Use the graph to

[ 3 ]

(i)

calculate a value for the acceleration of free fall close to the surface of the Moon.

[ 3 ]

any correct method used;
correct reading from graph;
1.6 to $1.7 \mathrm{~m} \mathrm{~s}^{-2}$ ;

(b)

Calculate the speed of an identical ball when it falls 3.0 m from rest close to the surface of Earth. Ignore air resistance.

[ 1 ]

$\quad 7.7 \mathrm{~m} \mathrm{~s}^{-1}$ ;

Exam points

Above escape speed, an unpowered projectile slows with decreasing deceleration and approaches a nonzero constant velocity far from the planet.
For release from rest, sketch displacement as a parabola; a larger downward acceleration gives more negative displacement at the same time.
With speed-dependent resistance, a coasting ship’s speed falls along a curve that becomes less steep as the resistive force decreases.
Explain why a constant-acceleration model fails by identifying a force that varies along the journey, such as changing solar-radiation intensity.

[Maximum number: 2]

This question is about the motion of a ship and observing objects from it.

The ship's engines are switched off and the ship comes to rest from a speed of $7 \mathrm{~m} \mathrm{~s}^{-1}$ in a time of 650 s .

It is unlikely that the acceleration of the ship will be uniform given that the resistive force acting on the ship depends on the speed of the ship. Using the axes, sketch a graph to show how the speed v varies with time t after the ship's engines are switched off.

starts at $7.0 / 7.2 \mathrm{~m} \mathrm{~s}^{-1}$ ;
(allow ECF from (d)(i))
correct shape;

Figure for Answer to Question 1 — IB Physics HL

Exam points

Resolve initial velocity using the angle’s stated reference: a vertical reference swaps the sine and cosine used for horizontal and vertical components.
Without resistance, horizontal velocity is constant and vertical velocity changes uniformly under gravity; keep its sign convention consistent.
For equal release heights and zero initial vertical velocity, fall time is independent of mass and horizontal launch speed.
At the highest point, vertical velocity is zero but downward acceleration remains; horizontal acceleration is zero throughout ideal flight.
For return to launch height, use twice the initial vertical component divided by g; the returning vertical velocity reverses sign.
Determine maximum rise from the initial vertical component, then add release height before comparing with a ceiling or obstruction.
Find time to a wall or net from horizontal distance divided by the horizontal velocity component.
Use that same time in the vertical equation and compare the resulting height with the net; a downward launch component needs the correct sign.
An alternative clearance test compares arrival time at the net with the time needed to fall to net height.
For horizontal projection, horizontal distance grows with time while vertical fall grows with time squared.
Identify which data determine range: horizontal velocity, initial vertical component and release height all matter for an oblique cliff launch.
For a horizontal launch, calculate fall time from height before using horizontal speed for range; changing mass alone has no effect.
Equal initial speed and equal launch height give equal impact speed without resistance, even when different launch directions give different flight times.
Recover total launch speed from horizontal distance, flight time and the cosine of the launch angle.
Add the initial height when converting vertical displacement into height above ground at a wall.

[Maximum number: 2]

A football player kicks a stationary ball of mass 0.45 kg towards a wall. The initial speed of the ball after the kick is $19 \mathrm{~m} \mathrm{~s}^{-1}$ and the ball does not rotate. Air resistance is negligible and there is no wind.

The ball leaves the ground at an angle of $22^{\circ}$ . The horizontal distance from the initial position of the edge of the ball to the wall is 11 m . Calculate the time taken for the ball to reach the wall.

horizontal speed $=19 \times \cos 22$ « $=17.6 \mathrm{~m} \mathrm{~s}^{-1}$ »
$\text { time }=\ll \frac{\text { distance }}{\text { speed }}=\frac{11}{19 \cos 22}=>0.62 \ll \gg$

Marking guidance:

Allow ECF for MP2

Exam points

For a falling object approaching terminal speed, its displacement–time gradient approaches a nonzero constant; displacement does not level off.
Combine weight with drag opposite the instantaneous velocity; the resultant force points along neither velocity nor drag alone.
On ascent, downward drag adds to weight and can make the downward vertical acceleration exceed g; horizontal acceleration is also nonzero.
For the given descent model, upward drag reduces downward acceleration below g; keep the chosen positive direction explicit.
Explain terminal speed through increasing drag and a vanishing resultant force, so acceleration becomes zero while speed remains nonzero.
At terminal speed, gravitational energy loss goes into thermal transfer or work against resistance rather than increasing kinetic energy.
For the given air-to-water drop, sketch speed rising before entry, then decreasing to a lower nonzero plateau before bottom contact.
With supplied F = kv², use terminal balance k = mg/v², or combine a nonzero-time tangent acceleration with mg − kv² = ma.
Sketch resultant force falling from a nonzero initial value towards zero; do not confuse it with the increasing drag force.

[Maximum number: 2]

In practice, air resistance affects the ball. Outline the effect that air resistance has on the vertical acceleration of the ball. Take the direction of the acceleration due to gravity to be positive.

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A.1.4—Distance and displacement1 question

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