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Question

A car travels first 30km with a uniform speed of 60 km/h and then next 30 km with a uniform speed of 40 km/h. Calculate :(i) the total time of journey, (ii) the average speed of the car.

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Solution

Answer : V1 = 60km/hr D1 = 30 km T1 = ? V2 = 40 km /hr D2 = 30 km T2 = ? Total Time = T1 + T2 We know that , velocity = Distance /Time Therefore , V1 = D1/T1 or T1 = D1 / V1 => T1 = 30 km / 60 km /hr = 1/2 hr V2 = D2/T2 or T2 = D2/ V2 => T2 = 30 km / 40 km /hr = 3/4 hr Hence , Total Time = T1 + T2 = 1/2 + 3/4 = 5/4 hrs we know that , Average Velocity = Total Distance / total time taken = 30 + 30 / 5/4 = 60/5/4 = 48 km /hr Hence Average Velocity is 48km/hr and total time of journey = 5/4 hours. My Short cut Method :- When a body travels equal distance with different velocities V1 and V2 , then Average Velocity is Calculated as Average Velocity = 2*V1*V2 / (V1 + V2 ) here , V1 = 60 km/hr and V2 = 40 km/hr therefore , Average Velocity = 2*60*40 / (60+40 )= 4800/100 = 48km/hr Also we know that , Average Velocity = Total Distance / Total Time Taken 48 = 60 / Total Time Taken or Total Time Taken = 60/48 = 5/4 Hrs . Read

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