A particle initially at rest moves along in a line so that its acceleration is a (t) = 10 / (t+1) for t>=0.

What is the velocity of the particle at time t=4?

Answer: 16.09m/s

Explanation:

Given the acceleration a (t) = 10 / (t+1), to derive the velocity function, we need integrate the acceleration function.

v (t) = integral{10/t+1}dt

Since all constants always come out of the integral, the equation becomes;

v (t) = 10integral{1/t+1}dt

One of the integral law is that if the numerator of the function to be integrated is the differential of the denominator, the resulting answer will be natural logarithm of the denominator i. e ln (t+1) since the denominator is ln (t+1) and if differentiated will give us 1 which is the numerator hence, the reason for the answer ln (t+1)

v (t) = 10ln (t+1)

@ t = 4, the velocity of the particle

v (4) = 10ln (4+1)

v (4) = 10ln5

v (4) = 16.09m/s²

Therefore, the velocity of the particle at time t=4 is 16.09m/s