A particle is moving in a straight line. The variation of position 'x' as a function of time 't' is given as x=(t³-6 t²+20 t+15) m. The velocity of the body when its acceleration becomes zero is :

Solution

Physics sir · 3 steps

Differentiate twice, set acceleration to zero to find the instant, then put that time into velocity.

1. Velocity. Differentiate the position once: v = dx/dt = 3t² - 12t + 20.
2. Acceleration. Differentiate again: a = dv/dt = 6t - 12. Setting a = 0 gives t = 2 s.

   v(2) = 3(2)² - 12(2) + 20 = 12 - 24 + 20 = 8 m s⁻¹

3. So. When the acceleration becomes zero, the velocity is 8 m s⁻¹, which is option (c).

The idea to keep. When a question names an instant by a condition, like zero acceleration, first solve that condition for t. Then put that t into whatever quantity is asked.

Answer from the NTA final answer key. Solution by PrepWiser.