Question

A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at $t=0$), the car was at $x=0$, where, $x$ is the position of the car at any time ‘$t$’.

The displacement of the car from the starting position will be

• A. $200\text{m}$
• B. $160\text{m}$
• C. $140\text{m}$
• D. $240\text{m}$

Answer 1

The correct option is B $160\text{m}$

As we know that, area under the $v-t$ curve gives the total displacement.
So, total displacement of the car is given as
$D=1/2\times 4\times 10+10\times 4+\frac{1}{2}\times 10\times (4+8)+1/2\times 20\times 8+1/2\times 20\times (-4)$
$=20+40+60+80-40$
$=160\text{m}$