Question

which equation of motion gives the velocity attained by a body in travelling a distance s​

Answer 1

Answer:

the equations ofotio. are;

1. v=u+at
2. s=ut+1/2at^2
3. v^2=u^2+2as

so....

answer is 3

Answer 2

Explanation:

S = ut +1/2 at ^2

The mathematically proven equations are as follows

(1) First equation of Motion:

V = u + at

soln.

Consider a body of mass “m” having initial velocity

“u”.Let after time “t” its final velocity becomes “v” due to

uniform acceleration “a”.

Now we know that:

Acceleration = change in velocity/Time taken

=> Acceleration = Final velocity-Initial velocity / time taken

=> a = v-u /t

=>at = v-u

or v = u + at

This is the first equation of motion.

(2) Second equation of motion:

s = ut + 1/2 at^2

sol.

Let the distance travelled by the body be “s”.

We know that

Distance = Average velocity X Time

Also, Average velocity = (u+v)/2

.: Distance (t) = (u+v)/2 X t …….eq.(1)

Again we know that:

v = u + at

substituting this value of “v” in eq.(2), we get

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

=>s = (2u+at)/2 X t

=>s = (2ut+at^2)/2

=>s = 2ut/2 + at^2/2

or s = ut +1/2 at^2

This is the 2nd equation of motion.

(or)

s=ut+1/2at²

Let me put this in simple words.

The first term u*t calculates the displacement due to initial velocity during the time interval t

Now, coming to the second term(1/2at²)

As we know acceleration is the rate of change of velocity,multiplying it with t i.e. a*t gives you the change of velocity during time interval t.

Adding this change in velocity to initial velocity gives the final velocity.

Now the answer to ‘why there is a 1/2 in the formula?’ :

Now that you know the initial and final velocities of the body, how will you find the distance traveled by it during the time interval?(given that the acceleration is uniform )

You can take the average velocity of the initial and final velocities and multiply it with time 't'( works only if the acceleration is constant throughout yhe time interval 't')

So the product of time 't' and average of change in velocity 'at/2' is at²/2

So the 1/2 is introduced during averaging of the change of velocity.

So,the Total displacement =ut+1/2at²