Free practice · 5 questions
Work through speed, acceleration, motion graphs and Newton’s second law. Show units at each step.
These are original InfinitySheets questions. Try each one first, then open the worked solution to check your method.
A cyclist travels 300 m in 25 s, stops for 10 s, then travels another 180 m in 25 s. Find the average speed for the whole trip.
Total distance is 300 + 180 = 480 m. Total elapsed time is 25 + 10 + 25 = 60 s. Average speed = 480 ÷ 60 = 8.0 m/s. The stop counts toward elapsed time even though no distance is covered.
A cart moving at 2.0 m/s reaches 8.0 m/s in 3.0 s at constant acceleration. Find the acceleration and distance travelled.
Acceleration is change in velocity divided by time, so (8.0 − 2.0) ÷ 3.0 = 2.0 m/s². With constant acceleration, the mean velocity is (2.0 + 8.0) ÷ 2 = 5.0 m/s. Multiply by 3.0 s to get 15 m.
Velocity rises uniformly from 0 to 6 m/s in 4 s, then stays at 6 m/s for another 5 s. Find the displacement.
Displacement is the area under the velocity–time graph. The first section is a triangle with area ½ × 4 × 6 = 12 m. The second is a rectangle with area 5 × 6 = 30 m. Total displacement is 42 m in the positive direction.
A 4.0 kg trolley is pulled right with 18 N. Friction acts left with 6 N. Find the trolley’s acceleration.
Take right as positive. The resultant force is 18 − 6 = 12 N. Using resultant force = mass × acceleration gives 12 ÷ 4.0 = 3.0 m/s² to the right. Use the net force rather than the pull alone.
A scooter travelling at 12 m/s brakes uniformly to rest over 18 m. Find its acceleration.
Use v² = u² + 2as with v = 0, u = 12 m/s and s = 18 m. Substitution gives 0 = 144 + 36a, so a = −4.0 m/s². The minus sign shows that the acceleration acts opposite the scooter’s direction of travel.
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