Question

A car having a mass of 500 kg is initially at rest. A constant 1,000 N net force acts on the car over a distance of 50 m, causing the car to speed up. After it travels 50 m, the car moves with constant velocity.

a.) What is the total work done on the car over the 50 m distance it travels while speeding up?
b.) How fast is the car moving after 50 m?
c.) What is the net force on the car while its moving with constant velocity?
d.) What is the total work done on the car while its moving with constant velocity?

Answer 1

(a) 50 kJ

(b) 14.14 m/s

(c) 0 N

(d) 0 J

Solution:

As per the question:

Mass of car, m = 500 kg

Force, F = 1000 N

Distance traveled, s = 50 m

Now,

(a) The total work done can be given as:

`W = F* s = 1000* 50 = 50000\ J = 50\ kJ`

(b) To calculate the speed of the car:

Using work-energy relation, we can say that the work done equals the change in the kinetic energy of the car:

`W = \Delta KE`

`(1)/(2)m(v'^(2) - v^(2)) = 50000`

where

v' = final velocity

v = initial velocity = 0

Now,

`(1)/(2)* 500v'^(2) = 50000`

`v' = √(200) = 14.14\ m/s`

(c) To calculate the net force on the car when the velocity is constant:

The net force is given as the product of mass and acceleration:

F = ma

Acceleration can be defined as the rate with which the velocity of the car changes and the since the velocity is constant, the car will not have any acceleration, a = 0

Thus the net force is also zero.

`F_(net) = 500* 0 = 0\ N`

(d) The total work done when the car moves with constant velocity:

`W = F_(net).s = 0\ J`