Question

A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be:

• A. $110m/s$
• B. $55m/s$
• C. $550m/s$
• D. $660m/s$

Answer 1

The correct option is B $55m/s$

Given,

$u=0m/s$ Particle initially at rest

Acceleration, $a=\frac{dv}{dt}$

$dv=adt$

$v=\int adt$. . . . . . . . .(1)

From the above equation, velocity of the particle is equal to the area under the acceleration-time curve.

From the given acceleration-time graph,

$v_{max}=\frac{1}{2}\times base\times height$

$v_{max}=\frac{1}{2}\times 11\times 10$

$v_{max}=55m/s$

The correct option is B.