Question

The position of a particle is given by the function s(t) = 2t² + 3t – 4. Find the time t = c in the interval 0 ≤ f ≤ 4 when the instantaneous velocity of the particle is equal to its average velocity in this interval.

Answer 1

Also, instantaneous velocity = ds/dt

∴ instantaneous velocity at t = c is (ds/dt)_{t = c} = 4c + 3

When instantaneous velocity at t = c equal to its average velocity, we get

4c + 3 = 11

4c = 8 

∴ c = 2 ∈ [0, 4] 

Hence, t = c = 2.