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The baseball is thrown up in the air with an initial velocity of 24 m/s. The gravitational force of attraction of the Earth decelerates the ball at a rate 9.8 m/s^2 in the downward direction.
The velocity of the ball at any instant of time t seconds after it was thrown up is given by `v_t = 24 - 9.8*t`
The ball continues to move up till its velocity is equal to 0 m/s. It then starts to fall down.
At the highest point that the ball can reach its velocity is equal to 0 m/s.
You are probably using v' to represent the initial velocity of the ball and v'' to represent the final velocity. If an object is accelerating and you know neither the duration of time for which it has been traveling nor the distance it has traveled, you cannot determine the final velocity of the object. A limiting case would be if the acceleration of the body is 0. In this case, the velocity of the object is always equal to its initial velocity.
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