KCET · Physics · Motion In One Dimension
A car covers the first half of the distance between two places at \(40\) km/h and another half at \(50\) km/h. The average speed of the car is
- A \(45.00\) km/h
- B \(44.44\) km/h
- C \(43.14\) km/h
- D \(42.04\) km/h
Answer & Solution
Correct Answer
(B) \(44.44\) km/h
Step-by-step Solution
Detailed explanation
Let the total distance be \(2d\).
Time taken to cover the first half of the distance is \(t_1 = \dfrac{d}{40}\).
Time taken to cover the second half of the distance is \(t_2 = \dfrac{d}{50}\).
Total time taken is \(t = t_1 + t_2 = \dfrac{d}{40} + \dfrac{d}{50} = \dfrac{9d}{200}\).
Average speed is given by the ratio of total distance to total time.
\(v_{avg} = \dfrac{2d}{\dfrac{9d}{200}} = \dfrac{400}{9} = 44.44\) km/h.
Answer: \(44.44\) km/h
Time taken to cover the first half of the distance is \(t_1 = \dfrac{d}{40}\).
Time taken to cover the second half of the distance is \(t_2 = \dfrac{d}{50}\).
Total time taken is \(t = t_1 + t_2 = \dfrac{d}{40} + \dfrac{d}{50} = \dfrac{9d}{200}\).
Average speed is given by the ratio of total distance to total time.
\(v_{avg} = \dfrac{2d}{\dfrac{9d}{200}} = \dfrac{400}{9} = 44.44\) km/h.
Answer: \(44.44\) km/h
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