# Exam-Style Questions on Kinematics

## Problems on Kinematics adapted from questions set in previous exams.

### 1.

GCSE Higher

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.

### 2.

GCSE Higher

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?

### 3.

GCSE Higher

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.

### 4.

IB Standard

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 $$t=5$$.

### 5.

GCSE Higher

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.

### 6.

IB Standard

The acceleration, $$a$$ ms-2 , of an object at time $$t$$ seconds is given by

$$a=\frac1t+4sin3t, (t\ge1)$$

The object is at rest when $$t=1$$.

Find the velocity of the object when $$t=7$$.

### 7.

IB Standard

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:

$$v=(t^2-5)^3$$

(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.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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Kausar Begum Khan, Kenya

Friday, January 26, 2018

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