Home
Class 12
PHYSICS
Function of displacement x and time t is...

Function of displacement x and time t is defined by equation `x = 2t^(3) - 3t^(2) – 4t + 1`. Acceleration will be zero at time

A

`0.5s`

B

2.0s

C

3.0s

D

4.0s

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `x = 2t^(3) - 3t^(2) - 4t + 1`
`therefore (dx)/(d t) = 6t^(2) - 6t - 4` = Velocity
Acceleration `= (d^(2)x)/(d t^(2)) = (d(6t^(2) - 6t - 4))/(d t^(2)) = 12t - 6`
If acceleration = 0 then, 12 t - 6 = 0.
`rArr t = (6)/(12) = 0.5 s`
Promotional Banner

Similar Questions

Explore conceptually related problems

The position x of a body is defined by equation x = Pt^(2)- Q t^(3) . The acceleration of the particle will be zero at time equal to

The angular displacement at any time t is given by theta(t) = 2t^(3)-6^(2) . The torque on the wheel will be zero at

A particle moves along a straight line such that its displacement at any time t is given by s = 3t^(3)+7t^(2)+14t + 5 . The acceleration of the particle at t = 1s is

The displacement of a particle is described by x = t + 2t^(2) +3t^(3) -4t^(4) The acceleration at t = 3s is

The displacement of a particle along an axis is described by equation x = t^(3) - 6t^(2) + 12t + 1 . The velocity of particle when acceleration is zero, is

The position of a body with respect to time is given by x = 4t^(3) – 6t^(2) + 20 t + 12 . Acceleration at t = 0 will be-

Equation of displacement for any particle is s = 3t^(3) +7t^(2) +14t8m . Its acceleration at time t = 1 sec is