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 maximum displacement from the starting position will be

• A. $200\text{m}$
• B. $250\text{m}$
• C. $160\text{m}$
• D. $165\text{m}$

Answer 1

The correct option is A $200\text{m}$

Positive increase in area of $v–t$ curve shows positive increase in displacement. So displacement is increasing till $t=50\text{s}$
$\Rightarrow$Max displacement = positive $v–t$ area.
$\therefore$ Max displacement $=1/2\times 4\times 10+10\times 4+\frac{1}{2}\times 10\times (4+8)+1/2\times 20\times 8$
$=20+40+60+80$
$=200\text{m}$