Question

15 th question what will be the solution

Answer 1

A particle moves along a straight line OX. At a time t, the distance x of the particle from O is given by x = 40 + 12t - t³

first of all, differentiate with respect to t,
$\frac{dx}{dt}=0+12-3t^2$

we know, change in distance per unit time is speed. so, $\frac{dx}{dt}=v=12-3t^2$
when speed of particle will be zero.
then, v = 12 - 3t² = 0, t = 2 [ but t ≠ -2]

now, distance covered by particle before coming to rest = distance covered by particle during 0 to 2sec.
= 40 + 12(2) - (2)³ - [40 + 12(0) -(0)³]
= 40 + 24 - 8 - 40
= 16m

hence, option ( d ) is correct.