Question

given s= t^3 -6t^2 find acceleration when body is at rest​

Answer 1

s = t³ - 6t²

velocity, v = ds/dt

= d/dt (t³ - 6t²)

= 3t² - 12t

when body is at rest

=> velocity = 0

=> 3t² - 12t = 0

=> 3t² = 12t

=> t = 4 s

then

acceleration, a = dv/dt

= d/dt (3t² - 12t)

= 6t - 12

therefore acceleration when body is at rest is given as

=> a = 6 x 4 - 12

=> a = 24 - 12

=> a = 12 m/s²