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 $t$.
Average speed from $t=0$ to $t=70s$ will be:

• A. $\frac{16}{7}$ $m/s$
• B. $\frac{24}{7}$ $m/s$
• C. $\frac{20}{7}$ $m/s$
• D. $0$

Answer 1

Answer: (A)

$\frac{16}{7}$ $m/s$

Average velocity is equal to the change in total displacement divided by total time taken. Total displacement is equal to the area under the velocity-time graph.

For $t=0$ to $t=70s$,

Displacement $s=\frac{1}{2}\times 10\times 4+10\times 4+\frac{1}{2}\times 10\times (4+8)+\frac{1}{2}\times 20\times 8+\frac{1}{2}\times 20\times -4$
$=20+40+60+80-40=160m$
Average velocity, $v=\frac{s}{t}$

$=\frac{160}{70}$ $=\frac{16}{7}m/s$