Q. Sketch a velocity-time graph for the motion of the body. From the graph explaining each step, calculate the total distance covered by the body


Answer:

Let a car is moving with a uniform velocity of 20 m/s for 20 seconds. Then brakes are applied and it comes to rest with uniform deceleration in 1 minute.

From the supposition, it is clear that the car has traveled 2 distances, which are following 

(1) Travelled with speed = v = 20 m s⁻¹ for t = 20 s

(2) Finally it moves with uniform deceleration  (retardation) and is stopped after (1 minute = 60 s)


Required to find:

Total Distance Traveled by car = S=?





Steps:  

1. Scale:

Choosing a suitable scale according to the above-given conditions
Along X-Axis:    One big division = 20 s
Along y-Axis:    One big division = 10 m s⁻¹ 

2. A graph is drawn below.




3. Distance calculation:

We know that the area of the trapezium (OABC) formed in the velocity-time graph is numerically equal to the total distance covered by the body. that is

Total Distance Travelled = area of the trapezium (OABC) of the graph

Total Distance Travelled = `\frac {1}{2}` ｘ {sum of the parallel sides} ｘ height of Trapezium

Total Distance Travelled = `\frac {1}{2}` ｘ {80 s + 20 s} ｘ 20 m s⁻¹ 

Total Distance Travelled = `\frac {1}{2}` ｘ {100 s} ｘ 20 ms⁻¹ 

Total Distance Travelled = 50 s ｘ 20 m s⁻¹ 

Total Distance Travelled = 1000 m



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