Figure A and B show the speed- time graphs of two cars (a) and (b) respectively. Using these graphs answer the following questions: (i) What is the acceleration of the car (a) and car (b) in the first two hours, the next two hours and in the last two hours? (ii) What is the total distance traveled by two cars? (iii) What is the average speed of two cars?

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 Acceleration is the rate of change of velocity. In other words,

acceleration = (final velocity - initial velocity) / (final time - initial time)

Thus, for car B, 

in first two hours: v = 40 km/h, u = 0 km/h and t = 2 h

thus, a = (40 -...

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 Acceleration is the rate of change of velocity. In other words,

acceleration = (final velocity - initial velocity) / (final time - initial time)

Thus, for car B, 

in first two hours: v = 40 km/h, u = 0 km/h and t = 2 h

thus, a = (40 - 0)/2 = 20 km/h^2

in next two hours: v = u = 40 km/h, thus, acceleration = 0 km/h^2

and in last 2 hours: v = 0, u = 40 km/h and t = 2 h

thus, acceleration = (0 - 40)/2 = -20 km/h^2.

Similarly, for car A,

in first two hours: acceleration = (30 - 0)/2 = 15 km/h^2

for next 2 hours, acceleration = (60 - 30)/2 = 15 km/h^2

and in the last 2 hours, acceleration = (0 - 30)/2 = -15 km/h^2

(ii) Total distance traveled by Car (B): 

Average velocity in first 2 hours = (0 + 40)/2 = 20 km/h

average velocity for next 4 hours = 40 km/h

and average velocity for last 2 hours = (40 + 0)/2 = 20 km/h

thus distance traveled = 20 km/h x 2 h + 40 km/h x 4 h + 20 km/h x 2 h

= 40 km + 160 km + 40 km = 240 km.

Similarly for car (A):

distance traveled = average speed x time = (0 + 30)/2  km/h x  2 h + (30 + 60)/2 km/h x 2 h + (60 +30)/2 km/h x 2 h + (30 + 0)/2 km/h x 2 h = 240 km

The distance traveled by both cars is same.

The distance traveled can also be determined as the area under the curve. For example, for car A: distance = area under the curve = area of triangle with base 8 hr and height 60 km/h = 1/2 x 8 h x 60 km/h = 240 km.

(iii) Average speed = distance traveled/time taken = 240 km/8 h = 30 km/h

Since both the cars traveled the same distance in the same time, the average speed is the same and is equal to 30 km/h.

Hope this helps. 

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