Question

The speed-time graph for a car is shown in Fig.
$\left(a\right)$ 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 the period.
$\left(b\right)$ Which part of the graph represents uniform motion of the car?

Answer 1

$\left(a\right)$

The total number of divisions on horizontal axis for $2s$ is $5$.

The total number of divisions on vertical axis for $2m/s$ is $3$.

The total displacement of the car during these two seconds will be given as the area under all these squares.

The area under the $(3\times 5)$ squares is given as:

$A_{15}=2\times 2=4$

So, the area under one small square is :

$A_1=\frac{4}{15}$

Now, the area under the graph for $4sec$ is:

the number of squares under the graph is :

$n=57$ small squares $+6$ half small squares

So, total number of squares $=60$.

So, the distance traveled by the car is the area under the curve.

$S=60\times \frac{4}{15}$

$S=16m$

$\left(b\right)$

The car moves under the uniform motion after the instant $t=6s$ because after this instant, the speed of the car becomes constant.