A) \[\frac{u+v}{2}\]
B) \[\frac{1}{2}\sqrt{{{u}^{2}}+{{v}^{2}}}\]
C) \[\sqrt{uv}\]
D) \[\sqrt{\left( \frac{{{u}^{2}}+{{v}^{2}}}{2} \right)}\]
Correct Answer: D
Solution :
| [d] Let S be the distance between two ends a be the constant acceleration |
| As we know \[{{V}^{2}}-{{u}_{2}}=2aS\]or\[aS=\frac{{{V}^{2}}-{{u}^{2}}}{2}\] |
| Let V be velocity at mid point. |
| Therefore, \[V_{c}^{2}-{{u}^{2}}=2a\frac{S}{2}\] |
| \[V_{c}^{2}={{u}^{2}}+aS\] |
| \[V_{c}^{2}={{u}^{2}}+\frac{{{V}^{2}}-{{u}^{2}}}{2}\] |
| \[{{V}_{c}}=\sqrt{\frac{{{u}^{2}}+{{v}^{2}}}{2}}\] |
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