Question

3) State the equations of motion along Yaxis​

Answer 1

Explanation:

The equations for linear motion is based on 2 assumptions namely:

•acceleration is uniform.

•the motion is in a straight line.

A body travelling at a velocity u accelerates uniformly for t seconds until its velocity attains a value v. The acceleration of the body is a

$a \: {ms}^{ - 2}$

and the distance travelled during the time t is s.

Derivation:

u : initial velocity

v : final velocity

t : time taken

a : acceleration

s : distance travelled

(1) For a uniformly accelerated body, average velocity is given by

$average \: velocity, <v> = \: \frac{u + v}{2}...equation \: 1$

(2) From the definition of acceleration,

$a = \frac{v - u}{t} \\ at = v - u \\ v = at + u...equation \: 2$

(3) Distance travelled,

$s = < v > t \\ from < v > =( \frac{u + v}{2}) t \\ substituting \: v = u+at \: in \: the \: above \: equation \\ s = ( \frac{u + u + at}{2} )t \\ = ( \frac{2u + at}{2} )t \\ s = ut + \frac{1}{2} a {t}^{2}...equation \: 3$

(4)

$substituting \: v =u + at \: into \: equation \: s = < v > t \\ v = u+ at \\ \frac{v - u}{a} = t \\ t = \frac{v - u}{a} \\ substituting \: above \: equation \: in \: \\ s = ( \frac{u + v}{2} )t \\ = ( \frac{u +v }{2})( \frac{v - u}{a} ) \\ s = \frac{ {v}^{2} - {a}^{2} }{2a} \\ 2as = {v}^{2} - {u}^{2} \\ {u}^{2} + 2as = {v}^{2} \\ {v}^{2} = {u}^{2} + 2as...equation \: 4$

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