Motion — Numerical Practice
Covers: v = s/t, average speed, distance-time and speed-time graphs, a = Δv/Δt, and free fall. 20 questions, tagged Core or Extended.
A. Speed and Average Speed
A car travels 150 km in 2.5 hours. Calculate its average speed in km/h.
A runner covers 200 m in 25 s. Calculate her speed.
A train travels at 120 km/h for 3 hours, stops for 30 minutes, then travels a further 60 km in 1 hour. Calculate its average speed for the whole journey.
Convert a speed of 20 m/s into km/h.
A cyclist’s average speed is 15 km/h over a 45-minute journey. Calculate the distance travelled.
B. Distance-Time Graphs
A distance-time graph shows a straight line from (0 s, 0 m) to (8 s, 64 m). Calculate the speed.
A distance-time graph shows an object at rest at 20 m from 0-5 s, then moving to 60 m by 15 s. Calculate its speed during the moving phase.
Describe the shape of a distance-time graph for an object that is decelerating to rest.
A distance-time graph shows a curve that becomes steeper over time. State what type of motion this represents.
C. Speed-Time Graphs and Area
A speed-time graph shows an object at a constant 12 m/s for 6 s. Calculate the distance travelled.
An object accelerates uniformly from 0 to 18 m/s in 4 s, then travels at a constant 18 m/s for a further 5 s. Calculate the total distance travelled.
An object decelerates uniformly from 20 m/s to rest in 5 s. Calculate the distance travelled.
Explain how the distance travelled can be found from a speed-time graph where the acceleration is not uniform (the line is a curve).
D. Acceleration
An object accelerates from 4 m/s to 22 m/s in 6 s. Calculate its acceleration.
An object decelerates from 30 m/s to 10 m/s in 8 s. Calculate its acceleration, and state whether this is an acceleration or a deceleration.
A speed-time graph shows a straight line from (2 s, 5 m/s) to (10 s, 29 m/s). Calculate the acceleration.
A car accelerates uniformly at 4 m/s² for 5 s, starting from rest. Calculate its final speed.
E. Free Fall and Terminal Velocity
A ball is dropped and falls freely (no air resistance) for 3 s. Calculate the speed it gains. (g = 9.8 m/s²)
An object falls freely from rest for 2.5 s (no air resistance). Calculate (a) its speed and (b) the distance it has fallen, using the area under its speed-time graph. (g = 9.8 m/s²)
Explain, using the shape of a speed-time graph, why a skydiver’s graph flattens out as they approach terminal velocity.
Mastery Test
Convert 25 m/s into km/h.
A car travels 90 km in 1.5 hours. Calculate its average speed.
A distance-time graph shows a line from (0 s, 0 m) to (5 s, 45 m). Calculate the speed.
An object accelerates at 3 m/s² for 8 s from rest. Calculate its final speed.
A speed-time graph shows a constant 10 m/s for 12 s. Calculate the distance travelled.
An object decelerates uniformly from 40 m/s to rest in 10 s. Calculate the distance travelled.
A ball falls freely from rest for 4 s. Calculate the speed it gains. (g = 9.8 m/s²)
A speed-time graph shows a line from (1 s, 3 m/s) to (6 s, 23 m/s). Calculate the acceleration.
Explain why the area under a speed-time graph gives the distance travelled.
An object accelerates uniformly from 0 to 12 m/s in 3 s, then decelerates uniformly back to rest over the next 2 s. Calculate the total distance travelled.
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