Question

Velocity of the particle in a rectilinear motion is given as $v=3t^4-5t$ in $\text{m/s}$. Find
(i) Acceleration at $2$ sec.
(ii) Average acceleration in $2$ sec.

• A. (i) $71m/s^2$
  (ii) $17m/s^2$
• B. (i) $81m/s^2$
  (ii) $18m/s^2$
• C. (i) $91m/s^2$
  (ii) $19m/s^2$
• D. (i) $61m/s^2$
  (ii) $16m/s^2$

Answer 1

The correct option is C (i) $91m/s^2$

(ii) $19m/s^2$
Given, $v=3t^4-5t$
(i) Acceleration at $2$ sec means we have to find out the instantaneous acceleration at $2$ sec
$\Rightarrow a\left(t\right)=\frac{dv\left(t\right)}{dt}=\frac{d(3t^4-5t)}{dt}=12t^3-5$
$\Rightarrow a{|}_{@t=2sec}=12\times 2^3-5=91m/s^2$

(ii) Average acceleration in $2$ sec is given by
$\overline{a}=\frac{(v_f-v_i)}{\Delta t}$
$v_f{|}_{@t=2sec}=3\times 2^4-5\times 2=38\text{m/s}$
$v_i{|}_{@t=0sec}=3\times 0^4-5\times 0=0\text{m/s}$
$\overline{a}=\frac{(v_f-v_i)}{\Delta t}=\frac{38-0}{2}=19m/s^2$