Question

derive all 3 equations of uniformly accelerated motion without graphical method​

Answer 1

$\huge{ \underline{ \underline{ \sf{kinematic \: equation \: for \: uniformly \: accelerated \: motion}}}}$

When a particleh moves in in a straight lined with constant accelerated,then the position ,time ,velocity and acceleration of the position are represented by equation known as kinematic equation of motion.

$\large{ \underline{ \underline{ \sf{ formulas}}}}$

For motion of a body moving with a uniform acceleration the following 3 equation . Give the relationship between

Initial velocity [v]

Acceleration [a]

Time[t]

Distance travelled[s]

$\cdot \: v = u + at$

$\cdot \: s = ut + \frac{1}{2} a {t}^{2}$

$\cdot \: {v}^{2} = {u}^{2} + 2as$

$\bold {\underline{1. \: v = u + at}}$

Let u be the initial velocity of the particle at t=0

v is the final velocity of the particle after time t

Consider two points A & B on the straight line corresponding to t=0 &t = t respectively.Draw BC

Perpendicular on time - axus alsi draw AC

perpendicular

From the slope,

Slope V-T graph = acceleration [a]

$a = \tan({ \theta})$

$= \frac{opp}{adj} = \frac{BC}{AC} = \frac{v - u}{t}$

$a = \frac{v - u}{t}$

$v - u = at$

${ \boxed{v = u + at}}$

[Hey,i didn't answer all three equation so please refer the attachment ☺]