AP EAMCET · PHYSICS · Motion In One Dimension
If a car travels \(40 \%\) of the total distance with a speed \(v_1\) and the remaining distance with a speed \(\mathrm{v}_2\), then average speed of the car is
- A \(\frac{1}{2} \sqrt{\mathrm{v}_1 \mathrm{v}_2}\)
- B \(\frac{v_1+v_2}{2}\)
- C \(\frac{2 v_1 v_2}{v_1+v_2}\)
- D \(\frac{5 v_1 v_2}{3 v_1+2 v_2}\)
Answer & Solution
Correct Answer
(D) \(\frac{5 v_1 v_2}{3 v_1+2 v_2}\)
Step-by-step Solution
Detailed explanation
\(t_1 = \frac{0.4D}{v_1}\) \(t_2 = \frac{0.6D}{v_2}\) \(v_{avg} = \frac{D}{t_1 + t_2}\) \(v_{avg} = \frac{D}{\frac{0.4D}{v_1} + \frac{0.6D}{v_2}}\) \(v_{avg} = \frac{1}{\frac{0.4}{v_1} + \frac{0.6}{v_2}}\) \(v_{avg} = \frac{v_1 v_2}{0.4v_2 + 0.6v_1}\)…
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