# Instantaneous Velocity Formula

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Instantaneous Velocity Formula

Velocity is a measure of how quickly an object moves from one position to another. If an object is accelerating or decelerating, the velocity of the object changes with time. The instantaneous velocity of an object is the velocity at a certain instant of time. Velocity is the change in position divided by the change in time, and the instantaneous velocity is the limit of velocity as the change in time approaches zero. This is equivalent to the derivative of position with respect to time. Instantaneous velocity is a vector, and so it has a magnitude (a value) and a direction. The unit for instantaneous velocity is meters per second (m/s).

v = instantaneous velocity (m/s)

v = vector change in position (m)

Δt = change in time (s)

dr/dt = derivative of vector position with respect to time (m/s)

Instantaneous Velocity Formula Questions:

1) A cat that is walking toward a house along the top of a fence is moving at a varying velocity. The cat’s position on the fence is . Position x is in meters, and time t is in seconds. What is the cat’s instantaneous velocity at time t = 10.0 s?

a. vx = – ?.?? m/s

2) A child kicks a ball horizontally, off the edge of a cliff. The horizontal position of the ball is given by the function x(t) = bt, where b = 6.0 m/s. The vertical position of the ball is given by the function y(t) = ct2, where c = -4.90 m/s2. At t = 4.0 s, what are the horizontal and vertical components of the instantaneous velocity?

a. vy = ??.? m/s

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