# Initial Velocity Formula

Velocity is the rate that the position of an object changes relative to time. Forces acting on an object cause it to accelerate. This acceleration changes the velocity. The initial velocity,v_{i} is the velocity of the object before acceleration causes a change. After accelerating for some amount of time, the new velocity is the final velocity, v_{f}.

*initial velocity = final velocity - (accelerationÃ—time)*

*v _{i} = v_{f} - at*

v_{i} = initial velocity (m/s)

v_{f} = final velocity (m/s)

a = acceleration (m/s^{2})

t = time between the start and end of the acceleration (s)

Initial Velocity Formula Questions:

1) A train is moving slowly through a city. Once outside the city, the engine accelerates at 0.40 m/s^{2} for 60.0 s. After this acceleration, the velocity of the train is 30.0 m/s. What was the initial velocity?

Answer: The initial velocity can be found using the formula:

*v _{i} = v_{f} - at*

v_{i} = (30.0 m/s) - (0.40 m/s^{2})(60.0 s)

v_{i} = (30.0 m/s) - (24.0 m/s)

v_{i} = (30.0 - 24.0) m/s

v_{i} = 6.0 m/s

The initial velocity of the train was 6.0 m/s.

2) Achild throws a ball straight up in to the air. It leaves the child's hand with a positive initial velocity v_{i}. The ball moves up to a maximum point, then reverses and falls to the ground. The final velocity of the ball is v_{f} = -14.7 m/s, taking down to be the negative direction. The time from when the ball leaves the child's hand to when it hits the ground is 2.00 s. What was the initial velocity of the ball, as it left the child's hand? Acceleration due to gravity is g = -9.8 m/s^{2} (down, so the value is negative).

Answer: The initial velocity can be found using the formula:

*v _{i} = v_{f} - at*

v_{i} = (-14.7 m/s) - (-9.8 m/s^{2})(2.00 s)

v_{i} = (-14.7 m/s) - (-19.6 m/s)

v_{i} = (-14.7 m/s) + 19.6 m/s

v_{i} = +19.6 m/s - 14.7 m/s

v_{i} = +4.90 m/s

The initial velocity of the ball was +4.90 m/s (up).

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