# Velocity Formula

Velocity is a measure of how quickly an object moves. So, the velocity is the change in the position of an object, divided by the time. Velocity has a magnitude (a value) and a direction. The unit for velocity is meters per second (m/s).

*v* = velocity (m/s)

*x _{f}* = the final position (m)

*x _{i}* = the initial position (m)

*t* = the time in which the change occurs (s)

Δ*x* = short form for "the change in" position (m)

Velocity Formula Questions:

1) A sail boat is in a 1000 m race, and it crosses the starting line when it is already at full speed. It reaches the finish line in exactly 1 minute and 20 seconds ( = 80.0 s). What is the velocity of the sail boat?

Answer: The initial position is the starting line, which we can give the value *x _{i} = 0.00 m*. The finish line is

*1000 m*from the start, so

*x*. The time it takes the sail boat to travel that distance is

_{f}= 1000 m*t = 80.0 s*. The velocity can be found using the equation:

*v = 12.5 m/s*

The velocity is *12.5 m/s*, in the direction of the finish line.

2) Each floor in a tall building is *3.00 m* high. When it's moving, the elevator in this building moves at a constant velocity of *1.50 m/s*. If the first floor is at position *0.00 m*, the second floor is at position *3.00 m*, and so on, how much time does it take for the elevator to go from the sixth (6^{th}) to the eighteenth (18^{th}) floor?

Answer: The initial and final positions of the elevator can be found using the floor numbers and the distance between floors. The initial floor is 6, so the initial position is:

*x _{i} = (6)(3.00 m)*

*x _{i} = 18.0 m*

and the final floor is 18, so the final position is:

*x _{f} = (18)(3.00 m)*

*x _{f} = 54.0 m*

The velocity (which we assume to be constant) is *v = 1.50 m/s*. The time must be found, so rearrange the equation:

*t = 24.0 s*

The time it takes for the elevator to travel from the sixth to the eighteenth floor is *24.0* seconds.

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