Question

Acceleration of a particle is given by a = t3 – 3t2
+ 5, where t = time in seconds and a =
acceleration in m/s2. Velocity of the particle
when t = 2 sec is 8 m/s. velocity of the particle
when t = 4 sec is
ans.
22 m/s
32 m/s
25 m/s
28 m/s​

Answer 1

Answer:

22 m/s

Explanation:

velocity = ∫a .dt

       = ∫(t³ - 3t² + 5) dt

       = (t⁴/4) - t³ + 5t + C

         

At t = 2,    velocity is 8 m/s

velocity = (2⁴/4) - 2³ + 5(2) + C

         8  = 4 - 8 + 10 + C

         2 = C

Therefore, at t = 4

velocity = (4⁴/4) - 4³ + 5(4) + C

   = 4³ - 4³ + 20 + 2     {C=2}

             = 22 m/s