Question

Exaplaintion S=ut+1/2a[t]2 formula

Answer 1

What is s=ut+1/2at^2?

This is the third equation of the three uniformly accelerated motion.

Here,

s is the distance

u is the initial velocity

a is the acceleration

t is the time

Let me derive this equation for you graphically.

In this graph,

v is the final velocity of the body and other variables have their usual significance.

We know,

Acceleration (a)= (v-u)/t

=>v-u=at…(eq.1)

Now,

Distance travelled in time t = Area of trapezium OABD

=Area of rectangle OAED+ Area of triangle ABE

=>S=OA*OD +1/2 BE*AE

=u*t+1/2*(v-u)*t

But from equation 1

v-u=at

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

Therefore,

S=ut+1/2at^2

Hope this helps you.What is s=ut+1/2at^2?

This is the third equation of the three uniformly accelerated motion.

Here,

s is the distance

u is the initial velocity

a is the acceleration

t is the time

Let me derive this equation for you graphically.

In this graph,

v is the final velocity of the body and other variables have their usual significance.

We know,

Acceleration (a)= (v-u)/t

=>v-u=at…(eq.1)

Now,

Distance travelled in time t = Area of trapezium OABD

=Area of rectangle OAED+ Area of triangle ABE

=>S=OA*OD +1/2 BE*AE

=u*t+1/2*(v-u)*t

But from equation 1

v-u=at

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

Therefore,

S=ut+1/2at^2

Hope this helps you.☺️