2. (15 points) A black 1997 Honda Civic is driving down the road. It has a mass

Question

2. (15 points) A black 1997 Honda Civic is driving down the road. It has a mass of 1100 kg. (4 pts.) It accelerates from a stop to a speed of 30 m/s. How much kinetic energy does it gain? (3 pts.) At the bottom of a hill the driver turns the engine off (don't do this!) and lets the car coast up a hill with a net vertical gain of 21 meters. How much gravitational potential energy did the car gain? (2 pts.) Ignoring air resistance and friction, how much kinetic energy does the car have left? (4 pts.) If there was no air resistance and friction, how fast would the car be going now? (2 pts.) In reality, the car rolls to a stop at the top of the hill. How much energy was lost to friction and air resistance?

Explanation / Answer

Mass of the car, m = 1100kg

velocity, v = 30m/s

Therefore, gain in kinetic energy= 1/2 mv2

= 1/2X1100X30X30

=495000 J

Net vertical gain, h = 21m

Gain in potential energy = mgh

= 21X9.8X1100  

= 226380 J

Kinetic energy left= 495000-226380 = 268620 J

The velocity of the car can be calculated by solving,

(1/2)mv2= kinetic energy left

v= sqrt( 2X268620/ 1100)

= 22.09 m/s

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