Question

The acceleration of a body is given in terms of the displacement s metres as a = 2s/(s^2 + 1)
Give a formula for the velocity as a function of the displacement given that when s = 1metres, v = 2ms^-1. Hence, find the velocity when the body has travelled 5 metres

Answer 1

integrate a for v, you get
v(s) = ln(s^2 + 1) + C

given when s = 1 v = 2
v(1) = ln(1 + 1) + C = 2
C = 2 - ln(2)

v(s) = ln(s^2 + 1) + 2 - ln(2)
v(5) = ln(26) + 2 - ln(2)
v(5) = ln(26/2) + 2 (rule of logs)
v(5) = ln(13) + 2
v(5) is about 4.565 m/s