Question

23. A particle starts from origin. If velocity is depending on
time as v = t - 6t, find its position at the moment
acceleration is zero.
(1) 18 m
(2)-27 m
(3)-18 m
(4) 27 m

​

Answer 1

answer : option (3) -18m

I think , velocity time relation is given, v = t² - 6t

we have to find the position at the moment, acceleration is zero.

we know, a = dv/dt

so, differentiate v with respect to time,

⇒ a = dv/dt = d(t² - 6t)/dt = 2t - 6

⇒a = 2t - 6

at a = 0 ⇒2t - 6 = 0

⇒t = 3 .....(1)

we know, ∫dx = ∫v.dt

⇒∫dx = ∫(t² - 6t)dt

⇒ x = t³/3 - 6t²/2 = t²/3 - 3t²

at t = 3

x = (3)³/3 - 3(3)² = 9 - 27 = -18

hence, position of particle at that moment is -18m