Question

A particle is moving along a straight line with constant acceleration and initial velocity of 10m/s. After some time, its velocity becomes 30m/s. Find out the velocity of the particle in the midpoint of its path.

Answer 1

Answer:

Initial velocity u = 10 m/s

Final velocity v = 50 m/s

When the body accelerated

Using equation of motion

....(I)

Now,The acceleration is reversed

Final velocity = 0

Initial velocity = 50 m/s

Using equation of motion again

.....(II)

The body starts moving in opposite direction from that point. after coming to the initial point.

The total distance s'' = s+s'

Let the velocity of the body is v'

Using equation of motion again,

Hence, The velocity of the particle is 70 m/s.

Explanation:

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Answer 2

let the total distance be 2x

Therefore distance up to mid point is equal to x.

Let the velocity at midpoint be v

And acceleration be a.

From equations of motion :

v² = 10² + 2ax............... 1)

30² = v² + 2ax.............. 2)

(2) - (1) gives :

30² - v² = v² - 10²

900 + 100 = 2v²

1000 = 2v²

v² = 1000/2

v² = 500

v = √500

v = 10√5 m/s