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# Power of an Engine.

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Tom drives a car to climb a 100 m up hill road with a slope of 30 degrees(from horizontal). The total mass of Tom and the car is 2000 kg. Tom wants to drive through this up-hill road in 10 s. You can assume g = 9.8 m/s^2, the friction, air drag, rolling resistance can be ignored. Please determine the engine power needed for Tom to drive this car through this up hill road for the following two cases.

(a) At constant speed? (Tip: you need to calculate the vehicle speed.)
(b) From rest to 20 m/s? (Tips: you need to consider kinetic energy and potential energy of the vehicle.)

##### Solution Summary

The power of engine required to climb up a hill is calculated for
(1) Motion with constant velocity
(11) Motion with constant acceleration.

##### Solution Preview

(a) As all other forces are to be ignored, the opposing force is only the weight mg of Tom and the car. The component of this force against the motion is mg sin(theta) and thus the force F needed to move it at constant speed is

F = mg sin(theta)

The speed ...

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