The velocity of a particle is given by v= t / t^2+3 ms^-1. If the particle is initially at the origin, find its displacement after 10s, correct to 2 decimal places.
Answer: 1.77 m
v(t) = ds/dt = t/(t^2+3)
so,
s(t) = 1/2 log(x^2+3) + c
since s(0) = 0, c = - 1/2 log3
so,
s(t) = 1/2 log((x^2+3)/3)
Now just plug in t=10
s(10) = 1/2 log(103/3)