Question

A 20.0-kg space probe fires an ion engine for 10.0 s during which time it experiences a force given by F(t) = (6.00 N/s2 )t2 i. If it was originally moving in the x-direction at 40.0 m/s, what is its velocity at t = 5.00 s?

Answer 1

190 m/s

Step-by-step explanation:

Acceleration = Force/ mass

a = F/m........................ Equation 1

Where F = force, m = mass of the space probe.

Given: m = 20 kg,

F(t) = 6.00t²

when t = 10 s.

F = 6.00(10)²

F = 600 N

Substituting these values into equation 1

a = 600/20²

a = 30 m/s.

But.

a = (v-u)/t

Where a = acceleration of the body, v = final velocity of the body, u = initial velocity of the body, t = time.

making v the subject of the equation,

v = u+at..................... Equation 2

Given: a = 30 m/s², u = 40 m/s, t = 5.00 s.

v = 40 + 30(5)

v = 40+150

v = 190 m/s

Thus the velocity of the space probe = 190 m/s