Question

If at time $t=0$, the initial velocity of a body is $5{\text{ms}}^{-1}$, then velocity at time $t=10\text{sec}$ if the $a-t$ for its motion as shown will be

• A. $55\text{m/s}$
• B. $50\text{m/s}$
• C. $65\text{m/s}$
• D. $70\text{m/s}$

Answer 1

The correct option is A $55\text{m/s}$

Given that,
Initial velocity, $u=5\text{m/s}$
From the graph
Acceleration, $a=5{\text{m/s}}^2$ (Constant for $10\text{min})$
Let the velocity of the particle at $t=10\text{s}$ is $v$
Now
$a=\frac{dv}{dt}$
$\Rightarrow \frac{dv}{dt}=5$
Integrating and substituting proper limits
$\Rightarrow \underset{5}{\overset{v}{\int }}dv=\underset{0}{\overset{10}{\int }}5dt$
$\Rightarrow v{|}_5^v=5t{|}_0^{10}$
$\Rightarrow v-5=50$
$\Rightarrow v=55\text{m/s}$

Alternate:

Change in velocity, $dv=$ Area under $a-t$ graph

$v-5=5\times 10$

$\Rightarrow v=55\text{m/s}$

Hence, option (a) is correct.