Question

Determine the amount of work done by the engine of a car with a mass of 2500 kg when it accelerates from 45 mph to 65 mph. (Use 1 mile = 1609 m).

Answer 1

amount of work done, W = 549.36 kJ

Given:

mass of a car engine, m = 2500 kg

initial velocity, u = 45 mph

final velocity, v = 65 mph

1 mile = 1609

Solution:

We know that 1 hour = 3600 s

Now, velocities in m/s are given as:

u = 45 mph =
`(45* 1609)/(3600)` = 20.11 m/s

v = 65 mph =
`(65* 1609)/(3600)` = 29.05 m/s

Now, the amount of work done, W is given by the change in kinetic energy of the car and is given by:

W =
`(1)/(2)m\Delta v^(2)`

W =
`(1)/(2)m* (v^(2) - u^(2))`

W =
`(1)/(2)2500* (29.05^(2) - 20.11^(2))`

W = 549.36 kJ