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Explain the terms uniform acceleration and average speed. a. A body at rest is given an initial uniform...

25. Explain the terms uniform acceleration and average speed.
a. A body at rest is given an initial uniform acceleration of 8.0 ms^-2 for 30 s after which the acceleration is reduced to 5.0 ms^-2 for the next 20 s. The body maintains the speed attained for 60 s after which it is brought to rest in 20 s. Draw the velocity-time graph of the motion using the information given above.
b. Using the graph calculate the:
(i) maximum speed attained during the motion.
(ii) average retardation as the body is being brought to rest.
(iii) total distance travelled during the first 50 s.
(iv) average speed during the same interval as in (iii).
25 (a) Explain what is meant by acceleration of free fall due to gravity, g.
(b) State two reasons why g varies on the surface of the earth.
(c) A stone is projected upwards at an angle 30° to the horizontal from the top of a tower 100m and hits the ground at a point Q. If the initial velocity of projection is 100ms^-1 calculate the:
(i) maximum height of the stone above the ground.

Answer

25. Uniform acceleration refers to a constant acceleration, meaning the velocity of an object changes at a constant rate. Average speed is the total distance traveled divided by the total time taken.

a. To draw the velocity-time graph, follow these steps:

  1. From 0 to 30 s, the velocity increases uniformly due to an acceleration of 8.0 ms-2.
  2. From 30 to 50 s, the velocity continues to increase but at a reduced acceleration of 5.0 ms-2.
  3. From 50 to 110 s, the velocity remains constant.
  4. From 110 to 130 s, the velocity decreases uniformly to zero.

b.

  1. Maximum speed attained during the motion:
    • First 30 s: v = u + at = 0 + 8.0 * 30 = 240 ms-1
    • Next 20 s: v = 240 + 5.0 * 20 = 340 ms-1
    • Maximum speed = 340 ms-1
  2. Average retardation as the body is being brought to rest:
    • Retardation = (Final velocity - Initial velocity) / Time = (0 - 340) / 20 = -17 ms-2
  3. Total distance travelled during the first 50 s:
    • First 30 s: Distance = 0.5 * 8.0 * 302 = 3600 m
    • Next 20 s: Distance = 240 * 20 + 0.5 * 5.0 * 202 = 4800 + 1000 = 5800 m
    • Total distance = 3600 + 5800 = 9400 m
  4. Average speed during the same interval as in (iii):
    • Average speed = Total distance / Total time = 9400 / 50 = 188 ms-1

25 (a). The acceleration of free fall due to gravity, g, is the acceleration experienced by an object when it is falling solely under the influence of gravity, typically measured as 9.8 ms-2 on Earth.

(b). Two reasons why g varies on the surface of the Earth:

  1. The Earth's rotation causes a centrifugal force that reduces g at the equator.
  2. The Earth's shape is not a perfect sphere; it is an oblate spheroid, causing variations in g.

(c). To calculate the maximum height of the stone above the ground:

  1. Vertical component of initial velocity = 100 * sin(30°) = 50 ms-1
  2. Maximum height from the top of the tower = (502) / (2 * 9.8) = 127.55 m
  3. Total maximum height above the ground = 100 + 127.55 = 227.55 m

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