Concepts Of Physics MCQ Edition [Volume 1]PhysicsRest and Motion Kinematics
A particle travels along the X-axis as x = u(t - 2 s ) + a(t - 2 s )^2 .
Options
- Athe particle's acceleration is a
- Bthe particle's initial velocity is u
- Cthe particle's acceleration is 2a
- Dat t = 2 s , the particle is at the origin
Correct answer
D. at t = 2 s , the particle is at the origin
Step-by-step solution
Given position x = u(t - 2) + a(t - 2)^2 Differentiating with respect to t , the velocity is v = dx dt = u + 2a(t - 2) Differentiating again, the acceleration is dv dt = 2a At t = 0 , the initial velocity is v = u + 2a(0 - 2) = u - 4a At t = 2 s , the position is x = u(2 - 2) + a(2 - 2)^2 = 0 , which means the particle is at the origin. Thus, the acceleration is 2a and at t = 2 s , the particle is at the origin.