Aparticle 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 < t < 1b. t > 1c. t > 0d. the velocity is never decreasing.

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.

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min