Question

The equation of displacement of a particle is $x\left(t\right)=5t^2-7t+3$. The acceleration at the moment when its velocity becomes $5m/sec$ is

• A. $3m/{sec}^2$
• B. $7m/{sec}^2$
• C. $10m/{sec}^2$
• D. $8m/{sec}^2$

Answer 1

The correct option is C $10m/{sec}^2$

Wehave
$x\left(t\right)=5t^2-7t+\mathrm{3...}\left(i\right)$
By differentiating both sides w.r.t $t$ we get
Velocity of the particle, $v=\frac{dx}{dt}=10t-\mathrm{7...}\left(ii\right)$
We have to find acceleration at the moment, when velocity becomes $5m/sec$
From Eq. (ii) we get
$10t-7=5$
$\therefore t=\frac{12}{10}$
Now, on differentiation both side of Eq(ii) w.r.t $t$,
we get acceleration of the particle
$\therefore a=\frac{dv}{dt}=10m/{sec}^2$
Here, acceleration is constant all the time
$\therefore a={\left|\frac{dx}{dt}\right|}_{t=\frac{12}{10}}=10m/{sec}^2$