Question

Prove that: S=ut +1/2at Square

Answer 1

Answer:

Suppose a boy has initial velocity u and final velocity V with uniform acceleration a and time t.

the distance travelled by the body in this time be s. The distance travelled by a moving body in time T can be found out by considering its average velocity.

Average Velocity = Initial Velocity + Final

Velocity/2.

That is, Average Velocity = v+u/2.

Also, Distance travelled = Average Velocity × Time.

So, S=(v+u)×t/2. ------- Equation 1.

Now, from equation 1 of motion we have v = u + at. Putting this value of v in equation 1 , we get :-

S=(u+u+at)×t/2

S=(2u+at)×t/2

S= 2ut/2 + at^2/2 ( 2 cancelled in 2ut/2)

Therefore, S=ut+1/2at^2.