An object moves with acceleration given by a = -6t^3 m/s^2. Its initial velocity at t = 0 is 5 m/s. How far will it move before stopping?
((((((The answer is " 7.5 m " )))))
Can you please show me the solution.
dv/dt = -6 t^3
v = -(6/4)t^4 + 5
when it stops, v = 0
t^4 = 3.333 seconds to stop
t = 1.351 and t^5 = 4.504
x = -(6/20) t^5 + 5 t
x = -(6/20)(4.504) + 6.755
= -1.3512 + 6.755
= 5.4 meters