Section 2: Motion and vectors

A cyclist rides once round a circular track of circumference 400 m and stops exactly where she started. What are the distance she has travelled and her displacement?

Which list contains only vector quantities?

A student walks 300 m due east in 200 s, then turns and walks 100 m due west in 100 s. What is her average velocity for the whole walk?

A car's velocity increases steadily from 8.0 m s⁻¹ to 20 m s⁻¹ in 4.0 s along a straight road. What is its acceleration?

A trolley moves in a straight line with a constant acceleration of 3 m s⁻². What does this mean?

The displacement-time graph shows a toy car moving along a straight track. Which describes its motion?

A displacement-time graph for a runner is a curve that gets steeper as time goes on. What does this show?

The velocity-time graph shows a scooter starting from rest. How far does it travel in the first 10 s?

A cyclist's velocity-time graph is a straight line from 15 m s⁻¹ at t = 0 to 0 m s⁻¹ at t = 6.0 s. Taking her direction of motion as positive, what is her acceleration?

Part of a velocity-time graph is a horizontal line above the time axis. What is the object doing during that part?

A ball is rolled up a smooth ramp. Its velocity-time graph is a straight line from +6.0 m s⁻¹ at t = 0 to −6.0 m s⁻¹ at t = 4.0 s, taking up the ramp as positive. What is its displacement at t = 4.0 s?

A go-kart moving at 2.0 m s⁻¹ accelerates uniformly at 1.5 m s⁻² for 5.0 s. What is its velocity at the end of the 5.0 s?

A train starts from rest and accelerates uniformly at 1.5 m s⁻² for 8.0 s. How far does it travel in that time?

A car travelling at 30 m s⁻¹ brakes with a uniform deceleration of 2.5 m s⁻² until it stops. How far does it travel while braking?

A stone is dropped from rest down a well and hits the water 1.2 s later. Ignoring air resistance and taking g as 9.8 m s⁻², how far does it fall?

A ball is thrown vertically upwards at 14 m s⁻¹. Ignoring air resistance and taking g as 9.8 m s⁻², how high does it rise?

A ball is thrown vertically upwards. Ignoring air resistance, which statement is true at the instant it reaches its highest point?

A cyclist starts from rest and accelerates uniformly at 2.0 m s⁻² for 5.0 s, then rides at the velocity she has reached for a further 10 s. How far does she travel in the 15 s?

A driver travelling at 25 m s⁻¹ sees a hazard. Her reaction time is 0.80 s, and the car then decelerates uniformly at 6.0 m s⁻². What is the total distance from seeing the hazard to stopping?

A student times a trolley rolling down a ramp and uses a light gate to find its velocity at four times, as in the table. Using the first and last readings, what acceleration do the results give?

A boat heads due north across a river at 4.0 m s⁻¹ relative to the water, while the river flows due east at 3.0 m s⁻¹. What is the boat's resultant velocity?

A kite string pulls on a child's hand with a tension of 12 N at 40° above the horizontal. What is the horizontal component of this force?

To derive s = ut + ½at², the area under a velocity-time graph for uniform acceleration from u to v in time t is split into a rectangle and a triangle. What does the triangle's area equal?

A student derives v² = u² + 2as. Starting from s = ½(u + v)t and t = (v − u)/a, which expression for s follows?

An aircraft climbs in a straight line at 200 m s⁻¹, at 30° above the horizontal. How long does it take to gain 1500 m of height?

Two forces of 5.0 N and 12 N act on the same point. The angle between them can be anything. What is the range of possible values for their resultant?

A force has a horizontal component of 12 N and a vertical component of 5.0 N upwards. What are the size and direction of the force?

To verify the law of addition of vectors, a small ring is held at rest by three spring balances pulling horizontally. Two of them pull at right angles to each other, reading 3.0 N and 4.0 N. If the law holds, what should the third balance read, and in what direction should it pull?

A stone is thrown vertically upwards at 12 m s⁻¹ from the edge of a cliff 25 m above the sea. It rises, then falls past the cliff edge into the sea below. Ignore air resistance and take g as 9.8 m s⁻². How long after it is thrown does it hit the sea?

A model rocket rises vertically from rest with a constant acceleration of 15 m s⁻² for 4.0 s. Its engine then stops and it coasts upwards, slowing at 9.8 m s⁻². Ignore air resistance. What is the greatest height it reaches?

Car A passes a set of traffic lights at a steady 20 m s⁻¹. At that instant car B, waiting at the lights, starts from rest with a constant acceleration of 2.5 m s⁻² in the same direction. How far from the lights is B when it catches A, so that the two cars are side by side?

A boat heads straight across a river 90 m wide, moving at 4.0 m s⁻¹ relative to the water. The water flows parallel to the banks at 3.0 m s⁻¹. How far downstream of its starting point does the boat reach the far bank?

A trolley's velocity-time graph has four straight sections: from 0 to 12 m s⁻¹ in the first 4 s; steady at 12 m s⁻¹ for the next 6 s; down to 0 in the next 3 s; then to −6 m s⁻¹ in the last 2 s. What is its displacement from the start at the end?

A car decelerates uniformly. It travels 60 m in the first 4.0 s after the brakes are applied and 20 m in the next 4.0 s, stopping at the end of that time. What was its speed when the brakes were applied?

Ball A is thrown straight up from the ground at 20 m s⁻¹. At the same instant ball B is dropped from rest from a point 40 m directly above. Ignore air resistance and take g as 9.8 m s⁻². Where do they meet?

A pilot wants to fly due north. The aircraft's speed relative to the air is 200 km h⁻¹, and a wind blows from the west at 50 km h⁻¹. In which direction must she point the aircraft, and what is its speed over the ground?

A card 0.050 m long on a trolley passes through two light gates 0.60 m apart. It blocks the first gate for 0.025 s and the second for 0.010 s. Assuming the acceleration is uniform, what is it?

A cyclist rides 6.0 km up a hill at a steady 10 km h⁻¹ and returns down the same road at a steady 15 km h⁻¹. What is her average speed for the whole trip?