question_answer

If a body moves for \[2\,\,s\] with \[15\,\,m/s\] velocity towards east and then moves with \[5\,\,m/s\] velocity for \[8\,\,s\] towards north, then average velocity is:

A)  \[5\,\,m/s\]                      

B)  \[15\,\,m/s\]

C)   \[30\,\,m/s\]                  

D)   \[7.5\,\,m/s\]

Correct Answer: A

Solution :

Key Idea: Average velocity\[=\frac{Displacement}{Time\,\,taken}\] Let body move along\[AB\], then\[BC\]. Distance travelled in\[2\,\,s\].                 \[{{S}_{1}}=15\times 2=30\,\,m\] Distance travelled in\[8\,\,s\]                 \[{{S}_{2}}=5\times 8=40\,\,m\] \[\therefore \]Displacement\[AC=\sqrt{{{(30)}^{2}}+{{(40)}^{2}}}\]                                       \[=\sqrt{900+1600}=\sqrt{2500}\]0                                       \[=50\,\,m\] Hence average velocity\[=\frac{displacement}{time\,\,taken}\]                                            \[=\frac{50}{8+2}=5\,\,m/s\]