Suppose that a particle moves along a line so that its velocity v at time t is given by this piecewise function:

Question

v(t)=5t if 0≤t<1
v(t)=6((t)^(1/2))-(1/t) if 1≤t

where t is in seconds and v is in centimeters per second (cm/s).
Estimate the time(s) at which the particle is 4 cm from its starting position

Answer 1

Assuming an initial position of zero,

s(t) = 5/2 t^2 for 0<=t<1
so, at t=1, s = 5/2
Now, using the 2nd function,

s(t) = 5/2 + 4t^(3/2) - log(t)
solve that for s(t) = 4