Question
an object's acceleration is given by the function a= 2/v^2, determine an expression for the velocity of the object as a function of time. (at t= 0, v=0)
Answers
drwls
dv/dt = 2/v^2
v^2*dv = 2 dt
Integrate both sides from t=0, v=0
v^3/3 = 2 t
v = [6 t]^1/3
Check: a = dv/dt = (1/3)*(6 t)^-2/3*6
= 2*(6t)^-2/3 = a/v^2
v^2*dv = 2 dt
Integrate both sides from t=0, v=0
v^3/3 = 2 t
v = [6 t]^1/3
Check: a = dv/dt = (1/3)*(6 t)^-2/3*6
= 2*(6t)^-2/3 = a/v^2