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Laws of motion equations Expert Answer
(1) Equation for velocity as a function of time.

Let us assume the motion is under uniform acceleration a.

Let u be initial velocity and v be the velocity after time t seconds.

Acceleration a is defined as rate of change of velocity ......................................(1)
above expression is rewritten as

v = u + ( a × t )  ....................................(2)

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(1) Equation for displacement as a function of time.

Let S be the distance travelled in t seconds with uniform acceleration a .

Let u be the initial velocity at time t = 0.

if v is the final velocity after t seconds , then average velocity = ( v + u ) /2

distance travelled S = average velocity × time ..................................(3)
If we substitute finale velocity v from eqn.(2) , then we get after simplifiaction ..................................(3)
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(3) Equation for final velocity v as a function of distance travelled S

Let us consider equation(2) as given above Let us substitute time t using eqn.(1) Above expression is simplified as

v2 = u2 + ( 2 a S )

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