Question

A car is moving on a straight road. The velocity of the car varies with time as shown in 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. $200$ $m$
• B. $250$ $m$
• C. $160$ $m$
• D. $165$ $m$

Answer 1

Answer: (A)

$200$ $m$

Displacement is positive when graph is above x-axis. Thus maximum displacement occurs at 50 second, till which graph is above axis. After that displacement needs to be subtracted from total. Thus maximum displacement = Area under curve till 50 seconds = Area of triangle till times 10 seconds + area of rectangle from time 10 seconds till 20 seconds + area of trapezium from time 20 seconds till 30 seconds + area of triangle from time 30 seconds till 50 seconds.
$s=\frac{1}{2}\times 4\times 10+4\times 10+\frac{1}{2}\times 10\times (4+8)+\frac{1}{2}\times 20\times 8$
$=20+40+60+80=200m$