Question

The acceleration-time graph for a particle moving along $x$-axis is shown in figure. If the initial velocity of particle is $-5\, m / s$, the velocity at $t=8\, s$ is.

• A. +15 m / s
• B. +20 m / s
• C. -15 m / s
• D. -20 m / s

Answer 1

Answer: (A)

The area under a-t graph gives change in velocity.
Given, $u=-5\, m / s$
$\Rightarrow $ Area on positive side
$=\frac{1}{2} \times 6 \times 10=30\, ms ^{-1}$
$\Rightarrow $ Area on negative side
$=\frac{1}{2} \times 2 \times 10=10\, ms ^{-1}$
Net area $=30-10=20\, ms ^{-1}$
$\Delta v=$ Area
$v-(-5)=20$
$\Rightarrow v=15\, ms ^{-1}$