Question

A graph of acceleration versus time of a particle starting from rest at $t=0$ is shown in the figure. The speed of the particle at $t=14$ second is

• A. $2m{s}^{-1}$
• B. $34m{s}^{-1}$
• C. $20m{s}^{-1}$
• D. $42m{s}^{-1}$

Answer 1

The correct option is B $34m{s}^{-1}$

Area under $a-t$ graph is change in velocity
Area$=\frac{1}{2}(4\times 4)+6\times 4+\frac{1}{2}\times 2\times 4-\frac{1}{2}\times 2\times 2$
$=36-2$
$=34m/s$
As initial velocity is zero therefore, the velocity at $14$ second is $34m/s$