Question

Velocity of the particle in a rectillinear motion is given as $v=2t^2-5t$ in $\text{m/s}$. Find
(i) Acceleration at $4$ sec.
(ii) Average accleration in $4$ sec.

• A. (i) $11m/s^2$
  (ii) $3m/s^2$
• B. (i) $7m/s^2$
  (ii) $2m/s^2$
• C. (i) $17m/s^2$
  (ii) $6m/s^2$
• D. (i) $16m/s^2$
  (ii) $7m/s^2$

Answer 1

The correct option is A (i) $11m/s^2$

(ii) $3m/s^2$
Given, $v=2t^2-5t$
(i) Accleration at $4$ sec means we have to find out the instantaneous acceleration at $4$ sec
$\Rightarrow a\left(t\right)=\frac{dv\left(t\right)}{dt}=\frac{d(2t^2-5t)}{dt}=4t-5$
$\Rightarrow a{|}_{t=4sec}=4\times 4-5=11m/s^2$

(ii) Average acceleration in $4$ sec is given by
$\overline{a}=\frac{(v_f-v_i)}{\Delta t}$
$v_f{|}_{t=4sec}=2\times 4^2-5\times 4=12\text{m/s}$
$v_i{|}_{t=0sec}=2\times 0^2-5\times 0=0\text{m/s}$
$\overline{a}=\frac{(v_f-v_i)}{\Delta t}=\frac{12-0}{4}=3m/s^2$