The velocity of a 640-kg auto is changed from 10.0 m/s to 44.0 m/s in 71.0 s by an external, constant force. (a) What is the resulting change in momentum of the car? kg · m/s (b) What is the magnitude of the force? N

(a) change in momentum of the car = 21760 kgm/s

(b) The magnitude of the force = 306.48 N

Explanation:

(a)

Change in momentum: This is the product of mass and change in velocity. The unit of momentum is kgm/s. It can be expressed mathematically as,

Change in momentum of the car = m (v-u) ... Equation 1

Where m = mass of the car, v = final velocity of the car, u = initial velocity of the car.

Given: m = 640 kg, v = 44.0 m/s, u = 10.0 m/s.

Substituting these values into equation 1,

Change in momentum of the car = 640 (44-10)

change in momentum of the car = 640 * 34

change in momentum of the car = 21760 kgm/s

change in momentum of the car = 21760 kgm/s

(b) Force: Force of a body can be defined as the product of mass and its acceleration. It is measured in Newton (N). It can be expressed mathematically as,

Force = ma ... Equation 2

Or

Force = m (v-u) / t ... Equation 3

Where m = mass of the car, v = final velocity of the car, u = initial velocity of the car, a = acceleration of the car, t = time taken to change the velocity.

Given: m = 640 kg, u = 10.0 m/s v = 44 m/s, t = 71 s.

Substituting these values into equation 3

Force = 640 (44-10) / 71

Force = (640*34) / 71

Force = 306.48 N

The magnitude of the force = 306.48 N