position of a particle moving in a straight line given by y= 3t^3+3t^2+5 then find acceleration of the particle at Time t=2s

position, y = 3 t³ + 3 t² + 5   ........................... (1)

 

velocity as a function of time is obtained by differentiating eqn.(1)

 

velocity v = dy/dt = 9 t² + 6 t ..........................( 2 )

 

acceleration as a function of time is obtained by differentiating eqn.(2)

 

acceleration a = d²y / dt² = 18 t + 6