A body has an initial velocity of $$3$$ $$m/s$$ and has an acceleration of $$1$$ $$m/sec2$$ normal to the direction of the initial velocity. Then, its velocity $$4$$ seconds after the start, is:

Correct option is 45 m/sec at an angle tan-1 (4/3) with the direction of initial velocity

Questions

A body has an initial velocity of 3 m/s and has an acceleration of 1 m/sec² normal to the direction of the initial velocity. Then, its velocity 4 seconds after the start, is:

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7 m/sec along the direction of initial velocity

7 m/sec along the normal to the direction of initial velocity

7 m/sec mid-way between the two directions

5 m/sec at an angle tan-1 (4/3) with the direction of initial velocity

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detailed solution

Correct option is D

ux=3m/s,ax=0uy=0, ay=1m/sec2 and t=4secIf vx and vy be the velocities after 4 sec respectively, thenvx=ux+axt=3ms−1vy=uy+ayt=0+1×4=4ms−1v=vx2+vy2=32+42=9+16=5m/sAngle made by the resultant velocity w.r.t. direction of initial velocity, i. e.,x-axis, isβ=tan−1⁡vyvx=tan−1⁡43

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