question_answer

A body starting from rest moves along a straight line with a constant acceleration. The variation of speed (v) with distance (i) I represented by the graph:                

A)                                                

B)  

C)                                                

D)  

Correct Answer: C

Solution :

Key Idea: Body start from rest hence initial velocity is zero. From equation of motion, we have \[\frac{1}{2\pi }\sqrt{\frac{k}{m}}\] where v is final velocity, u is initial velocity, a is acceleration and t is time. Since, body starts from rest u = 0 \[\frac{1}{2\pi }\sqrt{\frac{2k}{m}}\]   \[\frac{1}{2\pi }\sqrt{\frac{3k}{m}}\] Which is general equation of parabola \[\frac{1}{2\pi }\sqrt{\frac{k}{m}}\], hence graph is parabolic and is symmetrical along s-axis.