The speed-time graph for a car is shown here.

(a) Find how far does the car travel in the first 4 seconds. Shade the area on the graph that represents the distance travelled by the car during this period.

(b) Which part of the graph represents uniform motion of the car?

(a) The distance travelled by the car in the first 4 seconds is given by the area between the speed time curve and the time axis from t = 0 to t = 4 s

This area of the distance time graph which represents the distance travelled by the car

In order to find the distance travelled by the car in the first 4 seconds, we have to count the number of squares in the shaded part of the graph and also calculate the distance represented by one square of the graph paper.

We will now calculate the distance represented by 1 square of the graph.

If we look at the X-axis, we find that 5 squares on X-axis represent a time of 2 seconds.

5 squares on X-axis = 2 s

1 square on X-axis = s (i)

Now, if we look at the Y-axis,

We find that 3 squares on Y-axis represent a speed of 2 m/s

Now, 3 squares on Y-axis = 2 m/s

1 square on Y-axis = m/s (ii)

Since, 1 square on X-axis represents s and 1 square on Y-axis represent ms^-1

Therefore, Area of 1 square on graph = ×

= m

63 square represents distance = × 63

= 16.8 m

Therefore, the car travels a distance of 16.8 m in the first 4 seconds.

(b) In uniform motion, the speed of car becomes constant. The constant speed is represented by a speed time graph line which is parallel to the time axis. In the given figure, the straight line graph from t = 6 s to t= 10 s represents the uniform motion of the car. The part of graph representing uniform motion has been labelled AB.