IB Physics SL A.1 Kinematics Questions

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Practise IB Physics SL A.1 by translating position, velocity and acceleration between words, graphs and equations, including projectile components.

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

Exam points & syllabus

Exam points

Translate between motion graphs using gradients for rates, signed velocity–time area for displacement and acceleration–time area for Δv.
Find displacement from endpoint vectors; distinguish the travelled path, return-direction sign and net signed graph area.
Separate interval averages from instantaneous values: use total path or displacement over time, and a tangent for an instantaneous graph rate.
Use distances and speeds from one stated frame; for contact or catch-up, choose the relevant gap and relative motion.
Apply SUVAT to a constant-acceleration interval with signed initial velocity; keep launch height, reversals and the requested phase explicit.
Use position differences for a specified second, and constant-g symmetry or scaling to compare flight times, heights and speeds.
For staged or constrained motion, use the acceleration provided for that phase and match the two objects’ positions at catch-up.
Extract motion data over correctly matched time intervals; use several trace or flash positions and subtract the initial position.
Solve a drag-free projectile with one shared time: use horizontal motion for arrival, then vertical motion for height or clearance.
At a projectile apex retain horizontal velocity and downward acceleration; distinguish tangent velocity from the acceleration vector.
Compare projectile components and return conditions before comparing range, flight time or impact speed.
When acceleration changes, use the curve’s local slope and direction; a speeding-up object can have decreasing acceleration.
Explain terminal speed with zero resultant force or no further kinetic-energy gain, then distinguish its speed, acceleration and position graphs.
For parachute opening or water entry, show the change toward a lower terminal speed; keep downward motion distinct from upward acceleration.
Compare qualitative drag effects by components: ascent and descent acceleration, lower apex, steeper impact and delayed-drop separation.

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

Locate a rebound’s highest point where v = 0, while recognising that acceleration remains g.
Sketch rising height after a bounce with decreasing slope, ending at zero slope at maximum height.
Describe a repelled charge as moving away and speeding up even though its acceleration decreases.
Use signed area under a velocity–time graph to distinguish net displacement from distance travelled.
Read changing displacement–time slopes: decreasing slope means negative acceleration; constant slope means constant velocity.
Draw a projectile’s velocity arrow from the marked point, tangent to its path and pointing forwards.

[Maximum number: 3]

A ball of mass 0.250 kg is released from rest at time t=0, from a height H above a horizontal floor.

The graph shows the variation with time t of the velocity v of the ball. Air resistance is negligible. Take $g=-9.80 \mathrm{~ms}^{-2}$ . The ball reaches the floor after 1.0 s .

(a)

Label the time and velocity graph, using the letter M , the point where the ball reaches the maximum rebound height.

[ 1 ]

M at $1.6 \mathrm{~s}$

(b)

State the acceleration of the ball at the maximum rebound height.

[ 1 ]

« $g=>9.80<\mathrm{ms}^{-2} \gg$

Marking guidance:

Accept 9.81, 10 or a plain "g" Ignore sign if provided.

(c)

Draw, on the axes, a graph to show the variation with time of the height of the ball from the instant it rebounds from the floor until the instant it reaches the maximum rebound height. No numbers are required on the axes.

[ 1 ]

Exam points

Define instantaneous velocity as rate of change of position, rather than distance divided by time.
Add triangular and rectangular areas under acceleration–time graphs to find Δv or speed from rest.
Use velocity–time gradients to obtain acceleration, including a tangent estimate on a curved graph.
Choose position–time graph shapes whose changing gradients match the supplied velocity or speed.
Calculate average acceleration as (v − u)/Δt, keeping opposite velocity signs during a rebound.
Use Δx = vΔt within one stated frame; for approaching objects, use the rate of closing separation.

[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 « $\mathrm{m} \mathrm{s}^{-2}$ » (accept 9.6-10.0)

Exam points

Use endpoint geometry for projectile displacement or a circular-track chord, rather than path length.
Calculate net displacement from signed velocity–time areas, subtracting negative-velocity sections.
Explain negative displacement using the chosen positive direction; a negative value does not mean distance.
Find two objects’ separation from the difference of their velocity–time areas, allowing for delayed starts.

[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

Keep travelled distance positive on a return journey, but reverse the sign of endpoint displacement.

[Maximum number: 1]

The road from city X to city Y is 1000 km long. The displacement is 800 km from X to Y.

What is the distance travelled from Y to X and the displacement from Y to X ?

Distance travelled

from Y to X / km

Displacement from

Y to X / km

800

1000

800

-800

1000

-800

Exam points

Read instantaneous speed at the stated time, but calculate average speed as total distance divided by elapsed time.
Use path length for average speed and endpoint displacement for average velocity over the same interval.
Match the position–time tangent to the endpoint secant where instantaneous and average speed are equal.
Estimate instantaneous velocity from a tangent at the specified time, including its sign or direction.

[Maximum number: 3]

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

Choose a constant-acceleration equation using the stated initial velocity; do not assume u = 0.
Use s = ½(u + v)t for uniform launch or stopping motion, with the correct start and end speeds.
Use v² = u² + 2as when time is absent, including free-fall impact speeds and stopping distances.
Use s ∝ t² from rest: find distance in the next or nth second by subtracting cumulative distances.
Split acceleration and constant-speed stages, using a separate time interval for each distance.
Equate positions, not velocities, for catch-up problems: vt = ½at² gives the non-zero meeting time.
Solve signed vertical motion with the release velocity and height, including drops from rising balloons.
Use equal-height ascent/descent symmetry to find return time or infer launch speed from two crossing times.
Use the supplied constant acceleration in t = √(2s/a); do not substitute g for a constrained system.
Compare braking distances using changes in v²; dropping from v to v/2 leaves one-third of that distance.
Determine a or g from s = ½at² using matched timing intervals and a measured change in position.
Link uniform g to a straight v–t line and a quadratic displacement curve, preserving the chosen signs.
For projectile height, use the vertical launch component in y = y₀ + uyt − ½gt² and retain y₀.

[Maximum number: 2]

This question is in two parts. Part 1 is about the motion of a ship. Part 2 is about melting ice.

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 .

Estimate the distance that the ship takes to stop. Assume that the acceleration is uniform.

Exam points

Identify constant acceleration from equally increasing gaps between positions sampled at equal times.
State that free fall gives equal velocity changes, not equal displacements, in consecutive seconds.
Sketch a slowing ship’s v–t curve with decreasing slope magnitude as speed-dependent resistance falls.

[Maximum number: 2]

This question is in two parts. Part 1 is about the motion of a ship. Part 2 is about melting ice.

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 SL

Exam points

For a horizontal launch, find fall time from vertical motion and use the same time for horizontal range.
Resolve ux = u cosθ before using t = x/ux to find arrival time at a wall or net.
Use uy = u sinθ and add launch height to the maximum rise before deciding whether a ceiling is hit.
Check net clearance using signed vertical displacement at the time obtained from horizontal motion.
Keep vx constant and acceleration vertical; sketch vy changing linearly under the stated sign convention.
At the apex, keep vx and set vy = 0 before calculating momentum or kinetic energy.
For return to launch height, use T = 2u sinθ/g rather than the time based on the horizontal component.
At the original height on descent, retain ux = u cosθ but reverse uy to −u sinθ.
For equal horizontal momentum, compare speeds using p/m while keeping equal-height fall times unchanged.
Compare launch directions: equal initial speeds and fall heights can give equal impact speeds but different times.
After a horizontal-circle string breaks, combine initial horizontal motion with vertical gravitational fall.

[Maximum number: 5]

A student strikes a tennis ball that is initially at rest so that it leaves the racquet at a speed of $64 \mathrm{~m} \mathrm{~s}^{-1}$ . The ball has a mass of 0.058 kg and the contact between the ball and the racquet lasts for 25 ms .

(a)

The student strikes the tennis ball at point P . The tennis ball is initially directed at an angle of $7.00^{\circ}$ to the horizontal.

The following data are available.

[ 5 ]

(i)

Calculate the time it takes the tennis ball to reach the net.

[ 2 ]

horizontal component of velocity is $64.0 \times \cos 7^{\circ}=63.52<\mathrm{ms}^{-1} \gg$ $t=<\frac{11.9}{63.52}=>0.187 / 0.19<\mathrm{s} \gg$

Marking guidance:

Do not award BCA. Check working. Do not award ECF from using $64 \mathrm{~m} \mathrm{~s}^{-1}$ .

(ii)

Show that the tennis ball passes over the net.

[ 3 ]

ALTERNATIVE 1
$u_{y}=64 \sin 7 / 7.80<\mathrm{ms}^{-1} \gg$

decrease in height $=7.80 \times 0.187+\frac{1}{2} \times 9.81 \times 0.187^{2} / 1.63$ «m»

final height = « 2.80-1.63 » =1.1 / 1.2 «m»

«higher than net so goes over»

ALTERNATIVE 2

vertical distance to fall to net «=2.80-0.91 »=1.89 «m»

time to fall this distance found using $<1.89=7.8 t+\frac{1}{2} \times 9.81 \times t^{2}$ »

t=0.21 «s»

0.21 «s» > 0.187 «s»

«reaches the net before it has fallen far enough so goes over»

Other alternatives are possible

Exam points

Explain how a falling object can speed up while its acceleration decreases as drag builds.
Explain terminal speed using drag–weight balance, or GPE loss dissipated without further KE gain.
Choose acceleration graphs that fall toward zero as speed approaches its terminal value.
After a parachute opens, keep velocity downwards but acceleration upwards while the fall slows.
Choose a parachutist’s speed–time curve that rises from rest, then falls toward a lower terminal speed.
At terminal speed, draw distance–time motion with constant non-zero slope, not a horizontal plateau.
Explain why delayed identical drops separate at first, then keep a fixed gap once both reach terminal speed.
Sketch speed rising in air, dropping on water entry, then levelling at a non-zero terminal value.
Explain that drag adds to gravity on ascent but opposes it on descent when comparing vertical acceleration.
At an oblique apex, distinguish unchanged vertical acceleration g from the horizontal drag component.
Compare a drag-affected projectile with its ideal path: a lower apex and a steeper impact angle.

[Maximum number: 3]

This question is about kinematics.

After the stone in (a) hits the water surface it rapidly reaches a terminal speed as it falls through the water. The stone leaves Fiona's hand at time t=0. It hits the water surface at $t_{1}$ and it comes to rest at the bottom of the water at $t_{2}$ . Using the axes below, sketch a graph to show how the speed v of the stone varies from time t=0 to just before $t=t_{2}$ . (There is no need to add any values to the axes.)

straight line to water surface;
clear decrease after hitting surface;
constant non-zero speed reached smaller than maximum; $; \begin{aligned} & \text { (speed must be less than } \\ & \text { maximum velocity) }\end{aligned}$

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