Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'(t) is its velocity, and x''(t) is its acceleration.

Question

A particle moves along the x-axis at a velocity of v(t) = 5/√t, t > 0. At time t = 1, its position is x = 11. Find the acceleration and position functions for the particle.
a(t) =

Answer 1

v = 5 t^-.5 = 5/sqrt(t)
a = dv/dt = -2.5 t^-2.5

x = (5/.5)t^.5+c = 10 t^.5 + c

11 = 10 (1)^.5 + c
c = 1
so
x = 10 sqrt(t) + 1