# Mizoram Class 9 Answered

**Derive the equation of motion of a body in uniform acceleration using graphical method**

Asked by mateilrf | 19 Jan, 2021, 10:25: PM

Expert Answer

Acceleration a is defined as rate of change of velocity.

If at initial time t

_{o}, let the velocity be u and after time t , let the velocity be v.Acceleration a = ( v - u ) / ( t - t

_{o}) ..................(1)If acceleration is uniform then a is constant with respect to time.

From eqn.(1) , we get v = u + a ( t - t

_{o}) .................(2)Let us consider we start recording time from reference time instant t

_{o}, so that we consider t_{o}= 0Hence we get velocity as a function of time as , v = u + a t ...................(3)

Graph of eqn.(3) that gives velocity as a function of time is linear and it is given below

Area under the velocity-time graph between time τ =0 to time τ = t is the distance travelled by the object in time duration of t seconds.

As seen from graph given above, area under the graph between time τ = 0 to time τ = t is a trapezium OABC

Area of trapezium OABC = (1/2) [ OA + BC ] × OC ......................(4)

OA = inital velocity u ; BC = final velocity v ; OC = time duration t

Hence eqn.(4) becomes , Area OABC = (1/2) [ u+v ] × t

If S is distance travelled by object in time duration t , then above equation becomes ,

S = (1/2) [ u+v ] × t ........................(5)

If we substitute final velocity v from eqn.(3) , we get , S = (1/2) [ u + u + a t ] × t

Hence we get , S = u + (1/2) a t

^{2}.........................(6)If we want to eliminate t from eqn.(5) , we use eqn.(3) to substitute t as , t = ( v-u) /a ............(7)

Using eqn.(7) , we rewrite eqn.(5) as

S = (1/2) [ u + v ] ( v - u ) /a or v

^{2}= u^{2}+ ( 2 a S ) ............................(8)Eqn.(3) , Eqn.(6) and Eqn.(8) are equations of motion if acceleration is uniform

v = u + a t .................................(3)

S = u + (1/2) a t

^{2}.........................(6)v

^{2}= u^{2}+ ( 2 a S ) ......................(8)
Answered by Thiyagarajan K | 20 Jan, 2021, 10:36: AM

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Mizoram 9 - Physics

Asked by mateilrf | 19 Jan, 2021, 10:25: PM

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