A) \[\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}^{2}}}{t_{0}^{2}} \right)\]
B) \[\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}_{0}}}{t} \right)\]
C) \[mv_{0}^{2}\left( \frac{t}{{{t}_{0}}} \right)\]
D) \[mv_{0}^{2}{{\left( \frac{t}{{{t}_{0}}} \right)}^{3}}\]
Correct Answer: A
Solution :
| [a] \[{{v}_{0}}=a{{t}_{0}}\] \[\therefore \] \[a=\frac{{{v}_{0}}}{{{t}_{{}}}}\] |
| Velocity at any time t would be |
| \[V=at=\left( \frac{{{v}_{0}}}{{{t}_{0}}} \right)t\] |
| \[\therefore \] Kinetic energy, |
| \[\text{K=}\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m{{\left( \frac{{{v}_{0}}}{{{t}_{0}}} \right)}^{2}}{{t}^{2}}\] |
| From work energy theorem |
| \[W=K.E.\] |
| or \[W=\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}^{2}}}{t_{0}^{2}} \right)\] |
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