The given graph shows how the speed of a car changes with time:

(a) What is the initial speed of the car?
(b) What is the maximum speed attained by the car?
(c) Which part of the graph shows zero acceleration?
(d) Which part of the graph shows varying retardation?
(e) Find the distance travelled in the first 8 hours.

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Solution

(a) The initial speed of the car is 10 km/h at t=0.

(b) Speed of the car increases and attains a maximum speed of 35 km/h.

(c) Part BC of the graph shows zero acceleration because the velocity for that part is constant. As there is no change in velocity, so there is no acceleration.

(d) From point C to D, the velocity of the car is decreasing at a variable rate. So, the car has varying retardation from C to D.

(e) Distance travelled in first 8 hours will be the area under the speed-time graph from t = 0 to t = 8 h.

Distance travelled = Area under the trapezium (from t = 0 to t = 3) + Area under the rectangle (t = 3 to t = 8)

= $\frac{1}{2} \times 3 \times (10 + 35) + 5 \times 35 = 242.5 km$

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