Question

A particle is in motion and is accelerating. The velocity of the motion as a function of
time is given by: v(t)=(20t-5t2)m/s . Find
(a) The functional form of the acceleration,
(b) The instantaneous velocity at t = 3s, and
(c) The instantaneous acceleration at t = 3 s.

Answer 1

Given v(t) = 20t − 5t^2 (m/s).

(a) a(t) = dv/dt = 20 − 10t (m/s^2).

(b) v(3) = 20(3) − 5(3^2) = 60 − 45 = 15 m/s.

(c) a(3) = 20 − 10(3) = 20 − 30 = −10 m/s^2 (negative sign means the particle is decelerating at t = 3 s).