How to Find Average Velocity

Often calculating speed or average velocity is simply using the formula $speed$ $=$ $distance$ $time$ ${displaystyle {text{velocity}}={frac {text{distance}}{text{time}}}}$ $How to Find Average Velocity$ . But sometimes, you are given two different velocities for different periods of time or over different distances. For these cases, another formula is used to calculate the average velocity. Such types of problems can be useful in real life and often appear on standardized tests. Therefore, it will be very beneficial to learn these formulas and methods.

Table of Contents

Calculate average speed given distance and time

Rate the information given. This method is used when it is known:

total distance traveled by a person or vehicle; and
the total time it takes the person or vehicle to cover that distance.
Example: An travels 240 km in 3 hours, what is An’s average speed?

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Set up the formula for calculating velocity. That is

S

=

d

t

{displaystyle S={frac {d}{t}}}

S={frac {d}{t}}

, in there

S

{displaystyle S}

S

is the average speed,

d

{displaystyle d}

d

is the total distance and

t

{displaystyle t}

t

is the total time. ^{[1] X Research Source}

Substitute the distance into the formula. Remember that the distance here will be substituted for the variable

d

{displaystyle d}

d

.

For example, if An drove a total of 240 km, your formula would be: $S$ $=$ $240$ $t$ ${displaystyle S={frac {240}{t}}}$ $S={frac {240}{t}}$ .

Substitute time into the formula. Remember that time is substituted for variables

t

{displaystyle t}

t

.

For example, if An ran for 3 hours, your formula would be: $S$ $=$ $240$ $3$ ${displaystyle S={frac {240}{3}}}$ $S={frac {240}{3}}$ .

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/7/71/Calculate-Average-Speed-Step-6.jpg/v4-728px-Calculate-Average-Speed-Step-6. jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/7/71/Calculate-Average-Speed-Step-6.jpg/v4-728px-Calculate-Average-Speed-Step- 6.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div> “}

Divide distance by time. From this, the average speed per unit of time, usually hours, is obtained.

For example:
$S$ $=$ $240$ $3$ ${displaystyle S={frac {240}{3}}}$ $S={frac {240}{3}}$
$S$ $=$ $80$ ${displaystyle S=80}$ $S=80$
So, if An travels 240 km in 3 hours, his average speed will be 80 km per hour.

Calculate average speed when knowing multiple distances and corresponding time intervals

Rate the information given. This method is used when it is known:

many distances traveled; and
the amount of time it takes to travel each of those distances. ^{[2] X Research Source}
For example: An traveled 240 km in 3 hours, 190 km in 2 hours and 110 km in 1 hour, what is An’s average speed for the whole trip?

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/5/5b/Calculate-Average-Speed-Step-3-Version-3.jpg/v4-728px-Calculate-Average-Speed- Step-3-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/5/5b/Calculate-Average-Speed-Step-3-Version-3.jpg/ v4-728px-Calculate-Average-Speed-Step-3-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:” <div class=”mw-parser-output”></div>”}

Set up the formula for average velocity. My formula is

S

=

d

t

{displaystyle S={frac {d}{t}}}

S={frac {d}{t}}

, in there

S

{displaystyle S}

S

is the average speed,

d

{displaystyle d}

d

is the total distance traveled and

t

{displaystyle t}

t

is the total time. ^{[3] X Research Sources}

Determine the total distance. To do so, add up the number of kilometers covered for the entire trip. Substitute this value in

d

{displaystyle d}

d

in the formula.

For example, An traveled 240 km, 190 km, and 110 km, so you would determine the total distance by adding these three distances together: $240$ $+$ $190$ $+$ $110$ $=$ $540$ ${displaystyle 240+190+110=540}$ $240+190+110=540$ . The formula will become: $S$ $=$ $340$ $t$ ${displaystyle S={frac {340}{t}}}$ $S={frac {340}{t}}$ .

Determine the total time. To do so, add up the time, usually expressed in hours, that was spent traveling. Substitute this value in

t

{displaystyle t}

t

in the formula.

For example, since An traveled for 3 hours, 2 hours, and 1 hour, we would determine the total time by adding these three time parameters together: $3$ $+$ $2$ $+$ $first$ $=$ $6$ ${displaystyle 3+2+1=6}$ $3+2+1=6$ . So, the formula now will be: $S$ $=$ $540$ $6$ ${displaystyle S={frac {540}{6}}}$ $S={frac {540}{6}}$ .

Divide the total distance traveled by the total time spent traveling. The result obtained is the average velocity to find.

For example:
$S$ $=$ $540$ $6$ ${displaystyle S={frac {540}{6}}}$ $S={frac {540}{6}}$
$S$ $=$ $90$ ${displaystyle S=90}$ $S=90$ . So if you travel 240 km in 3 hours, 190 km in 2 hours and 110 km in 1 hour, then An’s average speed is 90 km/h.

Calculate average velocity when knowing multiple velocities with corresponding time intervals

Rate the information given. This method is used when it is known:

the speeds used by people or vehicles when moving; and
time using each of those speeds. ^{[4] X Research Sources}
Example: An moves at 80 km/h in 3 hours, 95 km/h in 2 hours and 110 km/h in 1 hour. What is An’s average speed for the entire journey?

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/5/5b/Calculate-Average-Speed-Step-3-Version-3.jpg/v4-728px-Calculate-Average-Speed- Step-3-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/5/5b/Calculate-Average-Speed-Step-3-Version-3.jpg/ v4-728px-Calculate-Average-Speed-Step-3-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:” <div class=”mw-parser-output”></div>”}

Set up the formula for average velocity. That is

S

=

d

t

{displaystyle S={frac {d}{t}}}

S={frac {d}{t}}

, in there

S

{displaystyle S}

S

is the average speed,

d

{displaystyle d}

d

is the total distance and

t

{displaystyle t}

t

is the total time. ^{[5] X Research Sources}

Determine the total distance. To do so, multiply each velocity by the corresponding time interval separately. The result is the distance traveled in each leg of the trip. Add up these distances. Substitute the total obtained in

d

{displaystyle d}

d

in the formula.

For example:
80 km/h for 3 hours = $80$ $\times$ $3$ $=$ $240$ $kilometer$ ${displaystyle 80times 3=240{text{km}}}$ $80times 3=240{text{km}}$
95 km/h for 2 hours = $95$ $\times$ $2$ $=$ $190$ $kilometer$ ${displaystyle 95times 2=190{text{km}}}$ $95times 2=190{text{km}}$
110 km/h for 1 hour = $110$ $\times$ $first$ $=$ $110$ $kilometer$ ${displaystyle 110times 1=110{text{km}}}$ $110times 1=110{text{km}}$
So the total distance traveled is $240$ $+$ $190$ $+$ $110$ $=$ $540$ $kilometer$ $.$ ${displaystyle 240+190+110=540{text{km}}.}$ $240+190+110=540{text{km}}.$ The formula will look like this: $S$ $=$ $540$ $t$ ${displaystyle S={frac {540}{t}}}$ $S={frac {540}{t}}$ .

Find the average speed when two velocities are traveling in equal time

Rate the information given. This method is used when it is known:

two or more different velocities; and
those velocities are used at equal intervals of time.
For example, if traveling 65 km/h in 2 hours and 95 km/h in another 2 hours, what is An’s average speed for the whole trip?

Set up the formula for average velocity when two velocities travel in equal intervals of time. That is

S

=

a

+

b

2

{displaystyle s={frac {a+b}{2}}}

s={frac {a+b}{2}}

, in there

S

{displaystyle s}

S

is the average speed,

a

{displaystyle a}

a

is equal to the velocity of the first half time and

b

{displaystyle b}

b

is the velocity for the remainder of the time. ^{[6] X Research Source}

In these cards, it doesn’t matter how long each velocity is used, as long as they are used for half the travel time.
You can adjust the formula when you know three or more velocities and these velocities are used at equal intervals. Such as, $S$ $=$ $a$ $+$ $b$ $+$ $c$ $3$ ${displaystyle s={frac {a+b+c}{3}}}$ $s={frac {a+b+c}{3}}$ nice $S$ $=$ $a$ $+$ $b$ $+$ $c$ $+$ $d$ $4$ ${displaystyle s={frac {a+b+c+d}{4}}}$ $s={frac {a+b+c+d}{4}}$ . As long as each velocity is used at equal intervals, your formula can follow this pattern.

Substitute speed into the formula. Where is

a

{displaystyle a}

a

and where is

b

{displaystyle b}

b

not important.

For example, if the initial speed is 65 km/h and the second speed is 95 km/h, your formula would be: $S$ $=$ $65$ $+$ $95$ $2$ ${displaystyle s={frac {65+95}{2}}}$ $s={frac {65+95}{2}}$ .

Add two velocities. Next, divide this sum by two. The result is the average speed of the whole trip.

For example:
$S$ $=$ $65$ $+$ $95$ $2$ ${displaystyle s={frac {65+95}{2}}}$ $s={frac {65+95}{2}}$
$S$ $=$ $160$ $2$ ${displaystyle s={frac {160}{2}}}$ $s={frac {160}{2}}$
$S$ $=$ $80$ ${displaystyle s=80}$ $s=80$
So if you move 65 km/h in 2 hours and then 95 km/h in 2 hours, An’s average speed is 80 km/h.

Find the average speed when the two velocities travel the same distance

Rate the information given. This method is used when it is known:

two different velocities; and
they are used for equal distances.
For example, if you drive 260 km to the water park at 65 km/h and come back 260 km at 95 km/h, what is the average speed of An’s entire trip?

Set up the formula for average velocity knowing that the two speeds are used for the same distances. That is

S

=

2

a

b

a

+

b

{displaystyle s={frac {2ab}{a+b}}}

s={frac {2ab}{a+b}}

, in there

S

{displaystyle s}

S

is the average speed,

a

{displaystyle a}

a

is the velocity in the first half of the distance and

b

{displaystyle b}

b

is the speed for the other half of the distance. ^{[7] X Research Sources}

The problem that requires this method often involves the question of a round trip.
In these types of cards, it doesn’t matter how far each speed is used, as long as they are used for half the distance.
You can adjust the formula knowing the three speeds are used for equal distances. Such as $S$ $=$ $3$ $a$ $b$ $c$ $a$ $b$ $+$ $b$ $c$ $+$ $c$ $a$ ${displaystyle s={frac {3abc}{ab+bc+ca}}}$ $s={frac {3abc}{ab+bc+ca}}$ . ^{[8] X Research Sources}

Substitute the velocity value into the formula. Where is

a

{displaystyle a}

a

and where is

b

{displaystyle b}

b

not important.

For example, if the initial speed is 65 km/h and the latter is 95 km/h, the formula would be: $S$ $=$ $($ $2$ $)$ $($ $65$ $)$ $($ $95$ $)$ $65$ $+$ $95$ ${displaystyle s={frac {(2)(65)(95)}{65+95}}}$ $s={frac {(2)(65)(95)}{65+95}}$ .

Multiply the product of two velocities by 2. That will be your fractional numerator.

For example:
$S$ $=$ $($ $2$ $)$ $($ $65$ $)$ $($ $95$ $)$ $65$ $+$ $95$ ${displaystyle s={frac {(2)(65)(95)}{65+95}}}$ $s={frac {(2)(65)(95)}{65+95}}$
$S$ $=$ $12350$ $65$ $+$ $95$ ${displaystyle s={frac {12350}{65+95}}}$ $s={frac {12350}{65+95}}$ .

Add two velocities. That will be your fractional denominator.

For example:
$S$ $=$ $12350$ $65$ $+$ $95$ ${displaystyle s={frac {12350}{65+95}}}$ $s={frac {12350}{65+95}}$
$S$ $=$ $12350$ $160$ ${displaystyle s={frac {12350}{160}}}$ $s={frac {12350}{160}}$ .

Simplify fractions. That will be the average speed for the whole trip.

For example:
$S$ $=$ $12350$ $160$ ${displaystyle s={frac {12350}{160}}}$ $s={frac {12350}{160}}$
$S$ $=$ $77$ $,$ $1875$ ${displaystyle s=77,1875}$ $s=77.1875$ . So if you drive 65 km/h for 260 km to get to the water park and then run back 260 km at a speed of 95 km/h, An’s average speed for the whole trip will be approximately 77 km/h.

Steps

Calculate average speed given distance and time

Calculate average speed when knowing multiple distances and corresponding time intervals

Calculate average velocity when knowing multiple velocities with corresponding time intervals

Find the average speed when two velocities are traveling in equal time

Find the average speed when the two velocities travel the same distance

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