Question

A point mass initially at rest moves along $x-$axis. Its acceleration varies with time as $a=6t+5m/s^2$. If its starts from origin, the distance covered by it in $1s$ is

• A. $3m$
• B. $5.5m$
• C. $3.5m$
• D. $5m$

Answer 1

The correct option is C $3.5m$

$a=6t+5$ $\Rightarrow \frac{dv}{dt}=6t+5$

$\int dv=\int (6t+5)dt$ $\Rightarrow v=3t^2+5t+c$

At $t=0$ , $v=0$ $\Rightarrow 0=3\times 0+5\times 0+c$ $\Rightarrow c=0$

$\Rightarrow \frac{dx}{dt}=3t^2+5t$

$\Rightarrow \int dx=\int (3t^2+5t)dt$ $\Rightarrow x=t^3+\frac{5}{2}{t}^2+c_1$

At $t=0$ , $x=0$ $\Rightarrow c_1=0$

$\Rightarrow x=t^3+\frac{5}{2}{t}^2$

At $t=1$, $\Rightarrow x=1+\frac{5}{2}=3.5m$