**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)

_{f}

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

_{i}

*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*_{f} = 1000 m. The time it takes the sail boat to travel that distance is *t = 80.0 s*. The velocity can be found using the equation:

_{i}= 0.00 m

_{f}= 1000 m

*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)

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

*x*_{i} = 18.0 m

_{i}= 18.0 m

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

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

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

*x*_{f} = 54.0 m

_{f}= 54.0 m