First, we must differentiate the following two concepts to avoid confusion:
At first glance, this looks like the same term, but in practice, it is not. Average speed asks you to know what is the general-classical average of the speed at which several drivers were traveling:
Example:
The average velocity of all drivers by adding the speeds and dividing by km/h.
What is the average speed according to the data?
Travel time: km/h: distance:
3 - 70 - 210
1 - 40 - 40
2 - 0 - 0
2.5 - 100 - 250
A man drives for two hours at a speed of 78 km/h, stops to get a coffee for fifteen minutes, and then continues for another hour and a half at a speed of 85 km/h.
What is his average speed?
In a relay race, three runners run one after another on a 450-meter track.
The first runner finishes in 1.5 minutes.
The second runner finishes in 1.35 minutes.
The third runner finishes in 1.42 minutes.
What is the average speed of the relay runners?
A truck driven by George makes its journey in two parts.
In the first part, its speed is 82 km/h and it travels for 4 hours.
Then, George has a break at a petrol station for 20 minutes.
In the second part, George travels at a speed of 70 km/h for 3 hours.
What is his average speed?
Gerard rides a motorcycle for 30 minutes over a distance of 40 km and continues for another 20 minutes at a speed of 70 km/h.
What is his average speed?
What is the average speed according to the data?
Travel time: km/h: distance:
3 - 70 - 210
1 - 40 - 40
2 - 0 - 0
2.5 - 100 - 250
Let's first remind ourselves of the formula for finding velocity:
= distance
= time
= velocity
Then substitute the data into the formula:
Calculate accordingly to get:
Therefore, the average velocity is 58.82.
58.82....
A man drives for two hours at a speed of 78 km/h, stops to get a coffee for fifteen minutes, and then continues for another hour and a half at a speed of 85 km/h.
What is his average speed?
In the first stage, we want to find the distance the truck traveled in its total journey,
We will use the data we already have,
78 km/h for two hours of driving and 85 km/h for an additional hour and a half.
78*2+85*1.5=
156+127.5=
283.5 km
Now, we want to discover the total duration of the journey.
We know there were two hours of driving, a quarter-hour break, and another hour and a half of driving,
Meaning:
2+0.25+1.5=
3.75 hours
Now, we'll divide the travel distance by the number of hours
285/3.75=
75.6 km/h
And that's the average speed!
km/h
In a relay race, three runners run one after another on a 450-meter track.
The first runner finishes in 1.5 minutes.
The second runner finishes in 1.35 minutes.
The third runner finishes in 1.42 minutes.
What is the average speed of the relay runners?
meters per second
A truck driven by George makes its journey in two parts.
In the first part, its speed is 82 km/h and it travels for 4 hours.
Then, George has a break at a petrol station for 20 minutes.
In the second part, George travels at a speed of 70 km/h for 3 hours.
What is his average speed?
km/h
Gerard rides a motorcycle for 30 minutes over a distance of 40 km and continues for another 20 minutes at a speed of 70 km/h.
What is his average speed?
km/h
A snail crawls for 7 minutes at a speed of 4 cm per minute, rests for 3 minutes, then continues to crawl a further 30 cm in 12 minutes.
What is its average speed?
Hugo participates in a swimming competition where he must swim 4 lengths of 25 meters.
He completes the first 25 meters in 43 seconds.
He swims the second length at a speed of 0.75 meters per second.
Then he stops to rest for 4 seconds, before finishing the last two lengths in 89 seconds.
What is his average speed?
Gary runs at a speed of 2 meters per second for 2 minutes, then stops for a minute and runs again for 2 minutes at the same speed.
What is the average speed?
Jonathan is reviewing his cycling records from his last competition.
During the first half hour, he rode at a speed of 28 km/h.
The following two hours, he rode at a speed of 24 km/h, then 15 minutes downhill at a speed of 32 km/h, before continuing for another hour at a speed of 27 km/h.
What was his average speed?
Hugo jogs around a circular path with a diameter of 750 meters 7 times.
The first two times he did it in \( 10\frac{1}{2} \) minutes.
For the next three laps, his speed is 9 km/h.
The last two laps takes him 12 minutes to complete.
What is the average speed?
A snail crawls for 7 minutes at a speed of 4 cm per minute, rests for 3 minutes, then continues to crawl a further 30 cm in 12 minutes.
What is its average speed?
cm per minute
Hugo participates in a swimming competition where he must swim 4 lengths of 25 meters.
He completes the first 25 meters in 43 seconds.
He swims the second length at a speed of 0.75 meters per second.
Then he stops to rest for 4 seconds, before finishing the last two lengths in 89 seconds.
What is his average speed?
meters per second
Gary runs at a speed of 2 meters per second for 2 minutes, then stops for a minute and runs again for 2 minutes at the same speed.
What is the average speed?
meters per second
Jonathan is reviewing his cycling records from his last competition.
During the first half hour, he rode at a speed of 28 km/h.
The following two hours, he rode at a speed of 24 km/h, then 15 minutes downhill at a speed of 32 km/h, before continuing for another hour at a speed of 27 km/h.
What was his average speed?
25.888...
Hugo jogs around a circular path with a diameter of 750 meters 7 times.
The first two times he did it in minutes.
For the next three laps, his speed is 9 km/h.
The last two laps takes him 12 minutes to complete.
What is the average speed?
km/h
A projectile is fired at a speed of 2500 km/h and travels 135 meters until it hits its target.
It passes through the target, which reduces its speed to 1300 km/h, after which point it continues for another 1.8 seconds until it hits a wall.
What is its average speed from the moment of firing until it stops?
Rodney rides a motorcycle for \( \frac{1}{3} \) of an hour over a distance of 30 km, stops to rest for \( \frac{1}{6} \) of an hour, then continues for \( \frac{1}{4} \) of an hour.
His average speed is \( 66\frac{2}{3} \) km/h.
How far does he ride in the last quarter of an hour of his trip?
The owner of a pizzeria suspects that one of his delivery drivers has taken too long of a break.
He knows that the driver traveled for 45 minutes at a speed of 90 km/h and then quickly returned the same way at a speed of 67.5 km/h.
In the middle, he took a break. The manager also knows that the driver's average speed throughout the day is 54 km/h.
How long was the break?
On the way home from school, Jerry stops at an ice cream shop.
It takes him 17 minutes to get to the shop, which is 1700 meters from his school.
It takes him a further 20 minutes to get from the shop to his house, which is 3000 meters away.
His average speed is 1.567 meters per second.
For how long did he stay at the ice cream shop?
Carmen climbs up a ladder for a minute and a half, stops for 15 seconds, then slides down a 3 meter-long slide in 20 seconds.
Her average speed from the bottom of the ladder to touching the ground is 0.036 meters per second.
How high is the ladder?
A projectile is fired at a speed of 2500 km/h and travels 135 meters until it hits its target.
It passes through the target, which reduces its speed to 1300 km/h, after which point it continues for another 1.8 seconds until it hits a wall.
What is its average speed from the moment of firing until it stops?
meters per second
Rodney rides a motorcycle for of an hour over a distance of 30 km, stops to rest for of an hour, then continues for of an hour.
His average speed is km/h.
How far does he ride in the last quarter of an hour of his trip?
km
The owner of a pizzeria suspects that one of his delivery drivers has taken too long of a break.
He knows that the driver traveled for 45 minutes at a speed of 90 km/h and then quickly returned the same way at a speed of 67.5 km/h.
In the middle, he took a break. The manager also knows that the driver's average speed throughout the day is 54 km/h.
How long was the break?
45 minutes
On the way home from school, Jerry stops at an ice cream shop.
It takes him 17 minutes to get to the shop, which is 1700 meters from his school.
It takes him a further 20 minutes to get from the shop to his house, which is 3000 meters away.
His average speed is 1.567 meters per second.
For how long did he stay at the ice cream shop?
minutes
Carmen climbs up a ladder for a minute and a half, stops for 15 seconds, then slides down a 3 meter-long slide in 20 seconds.
Her average speed from the bottom of the ladder to touching the ground is 0.036 meters per second.
How high is the ladder?
meters