Exam-Style Questions on Kinematics

Strat drove from Wolverhampton to London via Coventry.

• The distance from Wolverhampton to Coventry is 56 km.
• The distance from Coventry to London is 156 km.
• Strat's average speed from Wolverhampton to Coventry was 63 km/h.
• Strat took 90 minutes to drive from Coventry to London.

(a) Work out Strat's average speed for his total drive from Wolverhampton to London.

Raven drove from Bedrock to Springfield via South Park.

• Raven's average speed from Bedrock to South Park was 70 km/h.
• Her average speed from South Park to Springfield was 50 km/h.

Raven says that the average speed from Bedrock to Springfield can be found by working out the mean of 70 km/h and 50 km/h.

(b) If Raven is correct, what does this tell you about the two parts of Raven's journey?

Worked Solution

The following diagram shows a distance-time graph of the movement of a fish.

(a) Work out the average speed between 10 and 20 seconds.

(b) Estimate the speed of the fish at 25 seconds.

Worked Solution

Marilou and Sam had a skiing race. Here is Marilou’s speed-time graph from the start of the race.

(a) Marilou crossed the finishing line after a time of 40 seconds. How long was the race?

(b) Sam finished after a time of 50 seconds. What was his average speed, in kilometres per hour, for the race?

Worked Solution

A model train is placed on a length of straight track.

• It begins with constant acceleration for five seconds reaching a velocity of 6 m/s.
• It then slows down with constant deceleration of 1 m/s² for three seconds.
• It then slows down slightly more quickly coming to a complete rest after a further two seconds of constant deceleration.

(a) Draw a velocity-time graph for the train on graph paper provided below.

(b) Work out the total distance travelled by the model train.

Worked Solution

Pob and Wie are travelling from Bangkok to Khon Kaen.

Pob travels at a velocity given by \(V_P=50-t^2\), where t is in seconds and the velocity is in ms^-1.

Wie's displacement from Bangkok in metres is given by \(S_W=2t^2+70\).

When \(t=0\), both vehicles are at the same point.

Find Pob's displacement from Bangkok when \(t=5\).

Worked Solution

Here is a speed-time graph for a go kart.

Work out an estimate for the distance the kart travelled in the first 12 seconds by using six strips of equal width.

Worked Solution

The acceleration, \(a\) ms^-2 , of an object at time \(t\) seconds is given by

The object is at rest when \(t=1\).

Find the velocity of the object when \(t=7\).

Worked Solution

Very accurate equipment was used to measure the movement of a particle which moved in a straight line for 3 seconds. Its velocity, \(v\) ms^-1 , at time \(t\) seconds, is given by:

(a) Find the velocity of the particle when \(t=2\).

(b) Find the value of t for which the particle is at rest.

(c) Find the total distance the particle travels during the first three seconds.

(d) Show that the acceleration of the particle is given by \(a=6t(t^2-5)^2\)

(e) Find all possible values of t for which the velocity and acceleration are both positive or both negative.

Worked Solution