Question

What is uniform motion ? Derive the second equation of motion. (S = ut + ½ at2)​

Answer 1

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What is uniform motion ? Derive the second equation of motion. (S = ut + ½ at2)

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Derive the second equation of motion s = ut + (1/2)at^2 using the velocity-time graph. Derive the second equation of motion s = ut + (1/2)at2 using the velocity-time graph. Consider the linear motion of a body with an initial velocity u. Let the body accelerate uniformly and acquire a final velocity v after time t.

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A motion which covers equal distance in equal interval of time is called a Uniform motion.

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Answer 2

Answer:

A body has uniform motion if it travels equal distance in equal intervals of time, no matter how small these time intervals may be.

Explanation: The second equation of motion is ; s = ut + ½at². It gives the distance travelled by a body in time t.

Let's derive this second equation of motion.

Suppose a body has an initial velocity 'u' and a uniform acceleration 'a' for time 't' so that it's final velocity becomes 'v'. Let the distance travelled by the body in the time be 's'. The distance travelled by a moving body in time 't' can be found out by considering its average velocity. Since the initial velocity of the body is 'v' , the average velocity is ;

Average velocity = Initial velocity + final velocity/2

That is , Average velocity = u + v / 2

Also ,Distance travelled = Average velocity × time

so,

s = ( u + v ) / 2 × t

from the first equation of motion we have , v = u + at. Putting this value of v in equation ( 1 ) , we get

s = ( u + u + at ) × t / 2

or

s = (2u + at) × t/ 2

or

s = 2ut + at² / 2

or

s = ut + ½at²

where s = distance travelled by the body in time t

u = initial velocity of the body

and a = acceleration

This is second equation of the motion and it is used to calculate the distance travelled by a body in time t. should also be memorized because it will be used to solve numerical problems.

Hope this helps you.