Question

A 2.0 kg projectile with initial velocity v⃗  = 8.5 ı^ m/s experiences the variable force F = -2.0t ı^ + 4.0t² ȷ^ N, where t is in s.

Part A) What is the projectile's speed at t = 2.0 s?

Part B) At what instant of time is the projectile moving parallel to the y-axis?

Answer 1

a)

F = -2i + 4t^2

mdv/dt =  -2i + 4t^2j

2*dv/dt =  -2i + 4t^2j

dv/dt = -1i + 2t^2j

integrating with respect to t

dv/dt (from 8.5i to v) = -0.5*t^2i + (2*t^3 / 3)j

v - 8.5i = -0.5*t^2i + (2*t^3 / 3)j

at t = 2 sec

v = 6.5i + 16.3j

IvI = sqrt(6.5^2 + 5.3^2)

IvI = 8.4 m/s

b)

at this point x = 0

t^2/2 = 8.5

t^2 = 8.5 x 2

t = 4.12 sec