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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...

 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...

 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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