A particle moves along the x-axis so that at time t its position is given by s (t) = (t + 1) (t - 3) 3, t > 0. For what values of t is the velocity of the particle increasing? a. 0 0d. The velocity is never decreasing.

Answer: d. the velocity is never decreasing.

Therefore the velocity of the particle keeps increasing at a constant rate.

Since the velocity function is a Linear equation with a positive slope, the velocity is never decreasing.

Explanation:

Given;

The position function s (t) is given as;

s (t) = (t+1) (t-3) 3 = 3t^2 - 6t - 9

Velocity = change in position/change in time = ds/dt

ds/dt = differentiating the position function

ds/dt = 6t - 6

v (t) = ds/dt = 6t - 6

At t=0

v (t) = - 6

At t=1

v (t) = 0

At t=2

v (t) = 6

Acceleration = dv/dt = 6

Therefore the velocity of the particle keeps increasing at a constant acceleration of 6.

Since the velocity function is a Linear equation with a positive slope, the velocity is never decreasing.