Tuesday, 16 September 2014

ACCELERATION PROBLEMS AND SOLUTIONS


Problem 1:

You drive at a constant speed of 20 miles/h around a city block, checking out the neighborhood.  Are you accelerating?
  • Answer:
    Yes, the direction of the velocity vector is changing all the time.

Problem 2:

You are traveling east at 30 miles per hour.  You see a ball rolling onto the road and you break hard, because you are afraid that a child will come running after the ball.  You come to a stop in 0.8 seconds.  What is the direction of your average velocity in this short time interval?  What is your average acceleration?
  • Answer:
    The direction of your average velocity is east.  You are traveling east with decreasing speed until you come to a stop. The change in your velocity is Dv2-v= 0 - 30 mph east = -30 mph east = 30 mph west.  Let us convert to SI units.
    30 mph times 1609 m/mile times 1 h/(3600 s) = 13.4 m/s.
    Your average acceleration is  Dv/Dt = (13.4 m/s)/(0.8 s) west = 16.8 m/s2 west.