Question

(c) Prove mathematically second equation of motion.
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Answer 1

Answer:

It is denoted by

s= ut+1/2at^2

displacement = initial velocity * time +1/2 acceleration *time ^2

where,

s= distance travelled

u = initial velocity

t = time taken

a= acceleration

Derivation

we know that

velocity = displacement / time

velocity * time = displacement

displacement = velocity * time

if velocity is not constant

we can also take average velocity in place of velocity

so, our formula becomes

Displacement = average velocity * time

displacement = initial velocity + final velocity /2 * time.

s= (u+v/2) * t

from first equation of motion,

we know that v= u +at

putting value of v in this equation

s= [u+(u+at)/2] *t

s= (2u+at/2) *t

s= (2u/2+at/2)* t

s= (u +1/2at)*t

s= u+1/2at^2

Explanation:

I hope it's helpful to you