Question

Derive the following equations of motion for a body moving with uniform

acceleration in a straight line.

a) v=v 0+at

b) S=v0 t+
1/2
at2
c) v
2=v0^2+2 as

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Answer 1

Answer:

in this que we have to use graph to make equations

Hope it will help uhh!

Answer 2

Answer:

KINEMATIC EQUATIONS

V=V₀+at

S=V₀t+1/2at²

Explanation:

First equation

V=V₀+at

Let initial velocity (v₀), final velocity (v), time (t), acceleration (a) and displacement (S)

Acceleration is the rate of change of velocity.

$Acceleration=\frac{change in velocity}{ time }$

$a= \frac{final velocity-initial velocity}{time taken}$

$a=\frac{v-v_0}{t} \\at=v-v_0\\v=v_0+at$ ......................(1)

second equation:

S=V₀t+1/2at²

Distance traveled(S) = average velocity × time

$S=\frac{INITIAL VELOCITY +FINAL VELOCITY}{2}*TIME\\S=\frac{V_0+V}{2} *t$

From equation (1), v=u+at, substituting the values of v in the above equation.

$s=(\frac{v_0+v_0+at}{2} )*t\\\\=(\frac{2v_0+at}{2})*t \\\\s=V_0t+\frac{1}{2} at^{2}$