Given a constant acceleration and assuming linear motion, derive equations for velocity and position of a body with respect to time. explain what the integration constant represents.

v = at + u

Explanation:

acceleration, a = constant

As we know that acceleration is the rate of change of velocity

integrate on both sides

v = at + u

Where, u is the integrating constant and here it is equal to the initial velocity

Now we know that the rate of change of displacement is called velocity

Integrate on both sides

where, xo is the integrating constant which is initial position of the particle.

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