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THE EQUATIONS OF MOTION
     
1.   An object is initially moving at 10ms-1.
    At  t=0, it then accelerates uniformly to 25ms-1 in 5s.
It continues to move at this speed for 5s and finally comes to rest, with uniform acceleration, in 15s.
    First sketch a velocity against time graph for this motion, then calculate
a) the acceleration in the first 5s
  b) the total distance moved
  c) the acceleration in the last 15s
  d) the average speed for the whole motion.
     
2.   A table tennis ball is dropped from a height of about 30cm centimetres on to a hard, smooth, horizontal surface.
  a) Sketch a displacement against time graph for (about) the first two seconds of the motion of the ball (consider the displacement to be measured from the horizontal surface)
b) Sketch a velocity against time graph (covering the same period of time).
     
3.   A stone is dropped from a high building and it is observed to take 3.5s to reach the ground below.
  a) Assuming that air resistance is negligible, use the observation to calculate the height of the building.
  b) In practice, air resistance is not negligible.
    Is your answer to part a) higher or lower than the real height of the building?
    Explain your answer.
     
4.   At t=0s a stone is thrown vertically upwards and it reaches a height of 90m.
    Calculate
  a) the time taken to return for the stone to its starting point
  b) the speed with which the stone was thrown
  c) the speed of the stone when it was 50m above its starting point
  d) how far the stone will be from its starting point at t=7s.
     
5.   A person runs a 100m race in 12s.
    During the first 4s the person accelerates (for simplicity, assume that the acceleration is uniform).
    For the other 8s of the race the person runs at constant speed, v.
    Calculate the speed, v.
     
6. The diagram represents a series of photographs of a ball thrown upwards on a planet on which the acceleration due to gravity is not 9.8ms-2.
     
    The photographs were taken at 0.2s intervals. 
 
Calculate the magnitude of the acceleration due to gravity on the planet.
     
7.   At t=0, a body starts to fall from a height, h, in air.
    The acceleration due to gravity is 9.8ms-2.
    At t=8s, it reaches its terminal speed.
    At t=20s it hits the ground.
    Estimate the terminal speed of the body and the height h.
    State any assumptions or approximations you have made in your calculation.
 
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