Speed Physics: Definition, Formula & Units

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Speed Definition in Physics

Before continuing further, it will useful for us to establish a solid definition of speed.

Speed is a measure of the rate of change of the distance traveled by a moving object. speed is a scalar, which means that it is a unit of measurement that has magnitude but does not have direction.

The pace at which an object travels over a certain distance is known as speed.
A fast-moving item that has high speed, moves quickly, and covers a considerable distance in a short period.
A slow-moving item with a low speed, on the other hand, travels a comparatively little amount of distance in the same length of time.
A zero-speed object does not move at all.

A diagram of a scalar vs a vector. A scalar vs a vector. A scalar has magnitude, whereas a vector, like that shown above has magnitude and direction,Adapted from an image by Ducksters.

Velocity Definition in Physics:

Physicists utilize the basic concepts of speed and velocity to describe the motion of objects in terms of :

Distance
Time
Direction.

There are two unique meanings for these two words: speed and velocity. Nonetheless, we frequently hear these phrases used interchangeably.

It is true that speed is the pace at which an item moves along a route in terms of time.
Whereas velocity is the rate and direction of movement.

In other words, while speed is a scalar value, velocity is a vector, meaning that it is a unit of measurement that has both magnitude and direction.

For example, $50\;\mathrm{kmph}$ denotes the speed of a car driving along a road, whereas $50\;\mathrm{kmph}$ west denotes the velocity.

Speed Formula in Physics:

To calculate the speed of a moving object, we divide the distance traveled over the time needed to travel such a distance. $$v=\frac{d}{t}$$

Where $v$ is the speed, expressed in miles per hour ($\mathrm{mph})$,

$d$ is the distance traveled, expressed in miles.

and $t$ is the time. expressed in hours $\mathrm{h}$.

A little kid walks at a speed of $4\;\mathrm{kmph}$. How long does it take him to walk $20\;\mathrm{km}$? $$t=\frac{d}{v}=\frac{20\;\mathrm{km}}{4\;\mathrm{kph}}=5\;\mathrm{h}.$$

In two hours, a bicycle may cover a distance of $16\;\mathrm{mi}$. Estimate his speed. $$v=\frac{d}{t}=\frac{16\;\mathrm{mi}}{2\;\mathrm{h}}=8\;\mathrm{mph}.$$

If an automobile goes at $20\;\mathrm{mph}$, it takes $2\;\mathrm{h}$ to traverse a distance. What speed should it travel at in order to to same distance in $0.5\;\mathrm{h}$?$$d=20\;\mathrm{mph}\times2\;\mathrm{h}=40\;\mathrm{mi}$$

Speed required to cover the same distance in $0.5\;\mathrm{h}$: $$v=\frac{d}{t}=\frac{40\;\mathrm{mi}}{0.5\;\mathrm{h}}=80\;\mathrm{mph}.$$

Average Speed Formula in Physics

The following tables track the position of a moving object against time such that at each instant of time, the position relative to the start point is measured.

The first table represents the motion of an object moving at a constant speed.

Time (s)	Position (m)
$0$	$0$
$1$	$7$
$2$	$14$
$3$	$21$

An object with changing speed would have a table like the one below.

Time (s)	Position (m)
$0$	$0$
$1$	$4$
$2$	$12$
$3$	$20$

We can see that the difference between each pair of consecutive position measurements is increasing with time. This indicates that the speed was changing during the course of the object's motion. This means that the object does not have one speed for the whole of the journey, but has a constantly changing speed.

So we need a parameter that can be used to describe the overall changing speed of an object. One such measure is the average speed. Because the speed of a moving item changes often throughout its motion, it is typical to distinguish between the average and instantaneous speeds.

Moving things do not always travel at an unpredictable speed. An item will occasionally travel at a constant speed and a constant rate.

The speed at any given point in time is known as instantaneous speed.
The average speed is the sum of all instantaneous speeds divided by the number of different speeds; calculated when the speed of a moving object is changing with time.

Because the speed of a moving body is generally not constant and fluctuates over time, the formula for average speed is required. Even with changing speed, the total time and total distance traversed may be used, and we can get a single value to describe the complete motion using the average speed formula.

Taking the example of a moving car, the speed of the car may be:

accelerating from a stop
speeding up for a time
then slowing at a yellow light
and ultimately halting

At each instant, the speed of the car would reflect its motion at that respective moment of time.
However, one parameter can take into consideration all the speed variations above.
That parameter would be the average speed.

To calculate the average speed, we divide the total distance traveled over the total time needed.

Use the average speed formula to find the average speed of Tom, who travels the first $200\;\mathrm{km}$ in $4\;\mathrm{h}$ and the remaining $160\;\mathrm{km}$ in another $4\;\mathrm{h}$ using the average speed formula. To find the average speed, we need to calculate the total distance and the total time.

The total distance covered by Tom:

$$200\;\mathrm{km} + 160\;\mathrm{km}=360\;\mathrm{km}.$$

The total time is taken by Tom:

$$4\;\mathrm{h} + 4\;\mathrm{h}=8\;\mathrm{h}.$$

The average speed can be calculated: $$v_{\text{average}}=\frac{d_{\text{total}}}{t_{\text{total}}}=\frac{360\;\mathrm{km}}{8\;\mathrm{h}}.$$

After $3\;\mathrm{h}$ of driving at $30\;\mathrm{kmph}$, an automobile chooses to slow down to $20\;\mathrm{kmph}$ for the following $4\;\mathrm{h}$. Using the average speed formula, calculate the average speed.

The distance traveled the first $3\;\mathrm{h}$ can be calculated: $$d_{1}=vt=30\;\mathrm{kmph}\times3\;\mathrm{h}=90\;\mathrm{mi}.$$ The distance traveled for the second $4\;\mathrm{h}$ hours: $$d_{2}=vt=20\;\mathrm{kmph}\times4\;\mathrm{h}=80\;\mathrm{mi}.$$ The total distance traveled: $$d_{\text{total}}=d_{1}+d_{2}=80\;\mathrm{mi}+90\;\mathrm{mi}=170\;\mathrm{mi}.$$

Using the average speed formula : $$v_{\text{average}}=\frac{d_{\text{total}}}{t_{\text{total}}}=\frac{170\;\mathrm{mi}}{7\;\mathrm{h}}=24.3\;\mathrm{mph}.$$

Speed Units in Physics

As discussed earlier, speed refers to the rate at which an object changes its position. The speed can be measured or expressed in:

Meters per second $(\mathrm{m/s})$, where the distance will be expressed in meters and time in seconds.
Kilometers per hour $(\mathrm{kmph})$, where the distance is measured in kilometers and the time in hours.
Miles per hour $(\mathrm{mph})$, where the distance is expressed in miles and the time in hours.

More units can be used than the ones mentioned above, but they are the most frequently used.

Speed - Key takeaways

Speed is a scalar number that describes "the rate at which an item moves."
It is true that speed is the pace at which an item moves along a route in terms of time. Whereas velocity is the rate and direction of movement.
The speed at any given point in time is known as instantaneous speed.
Average Speed - the sum of all instantaneous speeds; calculated when the speed of a moving object is changing with time.
The term "speed" refers to the rate at which something moves. Meters per second $\mathrm{(m/s)}$, kilometers per hour $\mathrm{(kmph)}$, and miles per hour $\mathrm{(mph)}$ are the most frequently used units of speed $\mathrm{(mph)}$.
To calculate the speed, we divide the distance traveled by the time needed.
The same formula can be applied to calculate the average speed, where the speed would be varying with time.
In the case of average speed, we divide the total distance by the total time of travel