A) \[\frac{m{{v}_{1}}t}{{{t}_{1}}}\]
B) \[\frac{mv_{1}^{2}t}{t_{1}^{2}}\]
C) \[\frac{m{{v}_{1}}{{t}^{2}}}{{{t}_{1}}}\]
D) \[\frac{mv_{1}^{2}t}{{{t}_{1}}}\]
Correct Answer: B
Solution :
| [b] Let the constant acceleration of body of mass m is a. |
| From equation of motion |
| \[{{v}_{1}}=0+a{{t}_{1}}\] |
| \[\Rightarrow \]\[a=\frac{{{v}_{1}}}{{{t}_{1}}}t\] ...(i) |
| At an Instant t, the velocity v of the body |
| \[v=0+at\] |
| \[v=\frac{{{v}_{1}}}{{{t}_{1}}}t\] ...(ii) |
| Therefore, instantaneous power |
| \[p=Fv=mav\] \[(\because F=ma)\] |
| \[=m\left( \frac{{{v}_{1}}}{{{t}_{1}}} \right)\times \left( \frac{{{v}_{1}}}{{{t}_{1}}}.t \right)\] [from Eqs. (i) and (ii)] |
| \[=\frac{mv_{1}^{2}t}{t_{1}^{2}}\] |
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