Question

displacement of a body varies with time as S=√t find ratio of velocity of the body at t=4sec and t=1sec​

Answer 1

Explanation:

If motion is one dimensional,then magnitude of displacement i.e. shortest distances between initial and final positions is equal to the distance traveled. In such a case, the magnitude of instantaneous velocity i.e. velocity or speed at instant ‘t’ is equal to the rate of change of position of the object.

If at instant t the position of the object w.r.t. an origin ( a reference point) i.e. distance from the origin be s, the velocity of the object at instant ‘t’ is

v=dsdt

So distance traveled in infinitesimally small time interval dt is

ds=vdt

or

ds=(3t+4)dt

Distance in a finite time interval can be determined by using method of integration.

If we take the object initially situated at the origin i.e. at t=0, s=0, then distance traveled in 2 secs i.e. position of the object at instant t= 2 sec can be found as in the following mathematical steps:

∫s0ds=∫20(3t+4)dt

s=[3t22+4t]20

or

s=3×222+4×2

or

s=14m (if velocity is in m/s)