Question

Energy required to accelerate a car from 10 m/s to 20 m/s compared with that required to accelerate it from 0 to 10 m/s is

• A. twice
• B. thrice
• C. four times
• D. same

Answer 1

Answer: (B)

$ {{E}_{1}}=\frac{1}{2}m\,(v_{2}^{2}-v_{1}^{2}) $ $ \therefore $ $ {{E}_{1}}=\frac{1}{2}m\,[{{(20)}^{2}}-{{(10)}^{2}}] $ $ \Rightarrow $ $ {{E}_{1}}=\frac{1}{2}m\,(400-100) $ $ \Rightarrow $ $ {{E}_{1}}=\frac{1}{2}m\,\times 300=150\,m $ ?(i) $ {{E}_{2}}=\frac{1}{2}m\,[{{(10)}^{2}}-0] $ $ \Rightarrow $ $ {{E}_{2}}=\frac{1}{2}m\,\times 100=50\,m $ ?(ii) From Eqs. (i) and (ii), we have $ {{E}_{1}}=3{{E}_{2}} $