Question

A car is moving on a straight road with uniform acceleration. The speed of the car varies with time as follows :

Figure

Time (s)	:	0	2	4	6	8	10
Speed (m/s)	:	4	8	12	16	20	24

Draw the speed-time graph by choosing a convenient scale. From this graph :

(i) Calculate the acceleration of the car.
(ii) Calculate the distance travelled by the car in 10 seconds.

Answer 1

We have a velocity-time graph of a moving particle.

(i) We have to find the acceleration from the given graph.
Acceleration = slope of line
$=\frac{(12-4)}{(4-0)}\mathrm{m}/\mathrm{s}$² =2 m/s2
(ii) Distance travelled by the car is given by the area enclosed by the curve.
$$\begin{gathered} \mathrm{s}=\frac{(\mathrm{Sum}\mathrm{of}\mathrm{parallel}\mathrm{sides})\left(\mathrm{Height}\right)}{2} \\ =\frac{(4+24)\left(10\right)}{2}\mathrm{m} \\ =\boxed{140\mathrm{m}} \end{gathered}$$