the intial velocity of a particle is given by u (t=0)and the accleration by f, where f=at(here t is time and a is constant)which of the relations is valid?(a)v=u+at^2(b) v=u+at^2/2(c) v=u+at (d)v=u

Dear Suraj,

A very important concept in physics is the acceleration of an object. Acceleration is the rate at which an objects velocity is changing. This velocity could be changing because the object is slowing down, speeding up, turning around, or any combination thereof. If there is any change in the speed and/or direction of motion of an object, it is accelerating. Sometimes we only need the average rate of change of velocity, or average acceleration,

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Other times we may need the acceleration at a specific instant in time, or instantaneous acceleration, which is defined in terms of the average acceleration measured over an infinitesimally small elapsed time,

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As an object accelerates from an initial velocity v_i to a final velocity v_f, it may have many different values of instantaneous acceleration along the way. Basically, the average acceleration tells you what constant acceleration would produce the same velocity change v in the same amount of elapsed time t.

The change in velocity that results from a particular acceleration depends on how the velocity and acceleration relate to each other. In general, when the velocity and acceleration have opposite signs, the object in question will slow down. When the velocity and acceleration have the same sign (whether both are negative or positive), the object will speed up.

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If f=at, v is obtained by integrating f between limits u and v.

Integral of f from u to v= Integral of at from u to v = at^2/2 = v-u

Hence, v = at^2/2 + u. (b)