Carts a and b have equal masses and travel equal distances d on side-by-side straight frictionless tracks while a constant force f acts on a and a constant force 2f acts on b. both carts start from rest. the velocities a and b of the bodies at the end of distance d are related by

The velocity of cart B is the velocity of cart A

Solution:

As per the question:

Let the masses of both the carts A and B be 'm' kg

Distance traveled by both the carts be 'D' m

Force acting on A be 'F' N

Force acting on B be '2F' N

Now,

The relation between the velocities of A and B can be derived as :

Acceleration of cart A,

Acceleration of the cart B,

Now, using the third eqn of motion for both the carts A and B:

For cart A:

where

= initial velocity of cart A and cart B respectively

= final velocity of cart A

= final velocity of cart B

Now, dividing the velocities of the cart A and B:

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