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Question:

The speed-time graph for a car is shown in Fig. (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?

Solution:

(a)The total number of divisions on the horizontal axis for 2 s is 5. The total number of divisions on the vertical axis for 2 m/s is 3. The total displacement of the car during these two seconds will be given as the area under all these squares. The area under the (3×5) squares is given as: A₁₅ = 2 × 2 = 4 So, the area under one small square is: A₁ = 4/15 Now, the area under the graph for 4 sec is: the number of squares under the graph is: n = 57 small squares + 6 half small squares So, total number of squares = 60. So, the distance traveled by the car is the area under the curve. S = 60 × 4/15 S = 16 m (b) The car moves under uniform motion after the instant t = 6 s because after this instant, the speed of the car becomes constant.