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