# Speed and Velocity

Speed is the distance traveled per unit of time. Speed is the scalar quantity. It doesn't have a direction. A higher speed means an object is moving faster. A lower speed means it is moving slower. If it isn't moving at all, it has zero speed. The most common way to calculate the constant speed of an object moving in a straight line is the formula: $$v = {d \over t}$$ where $v$ is the rate, or speed $d$ is the distance moved $t$ is the time it takes to complete the movement This equation gives the average speed of an object over an interval of time. The object may have been going faster or slower at different points during the time interval, but we see here its average speed.
The instantaneous speed is the limit of the average speed as the time interval approaches zero. When you look at a speedometer in a car, you are seeing the instantaneous speed. While you may have been going 60 miles per hour for a moment, your average rate of speed for 10 minutes might be far more or far less.

#### Units for Speed

The SI units for speed are $m / s$ (meters per second). In everyday usage, kilometers per hour or miles per hour are the common units of speed. At sea, knots or nautical miles per hour is a common speed.

#### What is Velocity

Velocity is defined as the rate and direction of the change in the position of an object or the rate of change of displacement. In calculus terms, velocity is the first derivative of position with respect to time.
The most common way to calculate the constant velocity of an object moving in a straight line is the formula: $$v = {s \over t}$$ where $v$ is the velocity $s$ is the displacement $t$ is the time it takes to complete the movement

#### Speed vs. Velocity

Speed is a scalar quantity, it does not account for direction, while velocity is a vector quantity which is aware of direction. If ran across the room and then returned to your original position, you would have a speed - the distance divided by the time.
But your velocity would be zero since your position didn't change between the beginning and the end of the interval. There was no displacement seen at the end of the time period. You would have an instantaneous velocity if it were taken at a point where you had moved from your original position. If you go two steps forward and one step back, your speed isn't affected, but your velocity would be.
Fig.no.1: Speed vs Velocity
Here speed is the total distance covered (220m) in a specific time. While velocity can be calculated by observing the displacement (130m) in the same time interval.

#### Rotational Speed and Tangential Speed

Rotational speed or angular speed is the number of revolutions over a unit of time for an object traveling in a circular path. Revolutions per minute (rpm) is a common unit. But how far from the axis an object is (its radial distance) as it revolves determines its tangential speed, which is the linear speed of an object on a circular path. At one rpm, a point that is at the edge of a record disk is covering more distance in a second than a point closer to the center. At the center, the tangential speed is zero. Your tangential speed is proportional to the radial distance times the rate of rotation. Tangential speed = radial distance x rotational speed.

#### Relating Velocity, Speed, and Acceleration

Speed, velocity, and acceleration are all related to each other. Remember:
• Speed is a scalar quantity that indicates the rate of motion distance per time. Its units are length/time.
• Velocity is a vector quantity that indicates distance per time and direction. Like speed, its units are length/time, but direction is also cited.
• Acceleration is a vector quantity that indicates the rate of change of velocity. It has dimensions of length/time.
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