Sunday, 14 September 2014

SOLVING PROBLEMS USING EQUATION OF MOTION


1.  A rocketship coasting at 20,000 m/s in deep space fires its engines so that it accelerates at 20 m/s/s.
a)  How long will it have to keep accelerating to get to a speed of 300,000 m/s?
b)  How far will it travel while it is accelerating?

2.  The head of a rattlesnake can accelerate at 50 m/s/s when it strikes.  The rattlesnake’s head starts from rest and accelerates constantly until it strikes a victim that is 0.5 m away.
a)  How fast is the snake’s head moving when it hits the victim?
b)  How long does it take the snake’s head to get to the victim?

3.  A world land speed record was set by Colonel John P. Stapp on March 19, 1954 when he rode a rocket-propelled sled at 283.3 m/s.  The sled (and the colonel) was brought to a stop in 1.4s.  What acceleration did the colonel experience?

4.  Ben is inspired by Colonel Stapp’s example to take up rocket sledding.  He builds a track so he can get a modern rocket sled to go from rest up to 445 m/s. 
a)  If his track is only 225 m long, how quickly will Ben (and the rocket sled) have to accelerate to reach the target speed by the end of the track?
b)  How much time will it take the sled to go from one end of the track to the other?

5.  A high-speed train starts from rest and moves with constant acceleration.  As it passes a speed trap, a bored police officer uses a radar gun to measure the train’s speed as 30 m/s.  At another speed trap, 160 m further down the track, another officer measures the train’s speed as 50 m/s.
a)  How quickly was the train accelerating?
b)  How long did it take to travel the 160 m between speed traps?

6.  Cole is driving his car at 25.6 m/s along a dark road.  As he approaches a bridge, he notices several “Bridge Out” signs and hits the brakes.  Two seconds later, the car tumbles over the edge of the missing bridge, 34 m from where he noticed the signs.
a)  How fast was the car going when it tumbled off the bridge?
b)  How quickly was the car accelerating while it braked?

7.  A subway train accelerates gradually (a = 1.2 m/s/s) from rest at one station until it is halfway to the next station and then decelerates gradually (a = -1.2 m/s/s) for the final half of the trip until it comes to rest.  The two stations are 1100 m apart.
a)  What is the maximum speed the train reaches?
b)  How long does it take to travel between the stations?

8.  Heather is sitting in her car at a stoplight.  At the instant the light turns green, she starts accelerating at 2.2 m/s/s.  At the same moment a truck rumbles past her car going a constant speed of 12.2 m/s.  Heather is infuriated at being passed by a truck and she keeps accelerating until she gets ahead of the truck.
a)  How much time will it take her to catch up with the truck?
b)  How far down the street will she catch up with the truck?
c)  How fast will she be moving at this point?