A driver of a car travelling at 52 km h-1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km h-1 in another car applies his brakes slowly and stops in 10 s. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?
Case A:
Initial speed of the car, u1 = 52 km/h = 52 x (5 / 18) = 14.44 m/s
Time taken, t1 = 5 s
Final speed = 0 m/s
Case B:
Initial speed of the car, u2 = 3 km/h = 3 x (5 / 18) = 0.833 m/s ≅ 0.83 m/s
Time taken, t2 = 10 s
Final speed = 0 m/s
Plot of the two cars on a speed−time graph is shown in the following figure:
Distance covered by each car is equal to the area under the speed−time graph.
Distance covered in case A,
Distance covered in case B,
Then, the car1 travelling with a speed of 52 km/h travels farther after brakes were applied.
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Fig. 8.11
(a) Which of the three is travelling the fastest?
(b) Are all three ever at the same point on the road?
(c) How far has C travelled when B passes A?
(d) How far has B travelled by the time it passes C?
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The speed-time graph for a car is shown is Fig. 8.12.
Fig. 8.12
(a) Find how far does the car travel in the first 4 seconds. Shade the area on the graph that represents the distance travelled by the car during the period.
(b) Which part of the graph represents uniform motion of the car?
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(ii) the distance between the objects is doubled and tripled?
(iii) the masses of both objects are doubled?
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