Speed (medium and instantaneous)

The mako shark is considered the fastest animal in the ocean, it is capable of traveling 70 kilometers in one hour; Considering these data, could you calculate what their speed?

Italian scientist Galileo Galilei defined speed as:

speed formula

That is to say, speed is the distance covered per unit of time. Its magnitude is designated by the letter v.

Therefore, in our initial question we have:

  • How far did the shark travel? 70 kilometers.
  • How long did it take you to travel that distance? 1 hour.

Thus:

\ large v = \ frac {70km} {1h} = 70 \ hspace {0.2em} km / h

This means that the mako shark can swim at an extraordinary speed of 70 km / h. This is why it is known as the ocean cheetah!

Speed - Mako Shark
The mako shark, also called shortfin or shortfin mako, is considered the fastest animal in the ocean.

Speed units

Speed (also called speed) is a scalar magnitude, whose unit results from the combination of units of distance between time. At International system the meter per second is used, symbol m / s (the diagonal symbol “/” is read “by”, and means “divided by”), which is equivalent to the speed of a body that travels a length of 1 meter by 1 second.

Other units are:

  • Kilometer per hour or km / h; which is equivalent to the speed of a body that travels a length of 1 kilometer in 1 hour.
  • Miles per hour, whose abbreviation is mph (can also be found as my / h); equals the speed of a body that travels a length of 1 mile in 1 hour. It is officially used in the United States and the United Kingdom.
  • The knot (nautical mile per hour), whose abbreviation is kn (that comes from knot, knot in English); equals the speed of a body that travels a length of 1 nautical mile in 1 hour. It is used for air and sea navigation, as well as in meteorology to measure the speed of the wind.
  • Mach (M); 1 mach is the speed of sound in the medium in which the body moves. 1 mach is about 340m / s.
  • Speed (or speed) of light in a vacuum, whose symbol is c; it is a universal constant with the value of 299 792 458 m / s.

Speed unit conversions

  • 1 m / s = 3.6 km / h
  • 1 mph = 1,609 km / h
  • 1 kn t = 1,852 km / h = 0.514 m / s

What is instant speed?

Instantaneous speed is the speed at any instant of time. Therefore, it allows us to obtain information about the speed of a body or object at a specific point on the route.

Example of instantaneous speed

Police radars on freeways and highways measure the instantaneous speed of radar-targeted cars. So if a driver travels at 50 km / h, for a few seconds it increases to 90 km / h (more than the allowed limit) and then decreases to 60 km / h, and is stopped by the police for excessively quickly, it means that at the time it was targeted by the radar, its speed exceeded the allowed limit, regardless of whether seconds before or after it was traveling at the legal speed.

A driver can know the instantaneous speed of his car by observing the speedometer, since it gives a good approximation of this value.

Instantaneous speed - Speedometer
The speedometer shows us a good approximation of the value of the speed of the car.

What is the average speed?

Also called average speed, it is defined as the relationship between the total distance traveled and the total time spent during the trip without considering the particular details of the movement (if the speed was decreased, increased or stopped).

It is calculated through the formula:

Average speed formula

Example of average speed

If a person jogs for 1 hour and travels a distance of 10km, his average speed is 10 km / h. If another day you travel 10 kilometers in 1 hour, rest 2 minutes and then travel 5 kilometers in the following 58 minutes, your average speed during the two hours is:

\ large Speed \ hspace {0.3em} average = \ frac {10km + 0km + 5km} {2h} = 7.5 \ hspace {0.2em} km / h

The average speed does not indicate the various speeds or possible variations during short time intervals, but the average.

Difference between average and instantaneous speed

Suppose that a bus travels from one city to another and covers a distance of 400 km in 8 hours; Does it mean that it moved throughout the journey at 50 km / h? Not necessarily. It may be that the motorway was moving at 100 km / h but when it came out it decreased to 60 km / h and even, if it later found a red light at the traffic light, it would reach 0 km / h and some time later at 40 km / h. Each of these values is an instantaneous speed measurement.

Quick exercises

  1. What is your speed if you walk 2 meters every 0.5 seconds?

From the statement we know:

  • Distance = 2 meters
  • Time = 0.5 seconds

Thus:

\ large v = \ frac {2m} {0.5s} = 4 \ hspace {0.1em} m / s

Your speed is 4 m / s.

  1. How far do you travel if you maintain an average speed of 20m / s for 60 seconds?

From the statement we know:

  • Average speed = 20 m / s
  • Time = 60 seconds

How:

\ large Speed \ hspace {0.3em} mean = \ frac {Distance \ hspace {0.3em} total \ hspace {0.3em} traveled} {Time \ hspace {0.3em} of \ hspace {0.3em} traveled}

The distance traveled will be the average speed multiplied by the travel time:

Speed exercise

You cover a total distance of 1200 m.

  1. Calculate the total time (in seconds) it takes for a mako shark to travel 4 km at an average speed of 60 km / h.

From the statement we know:

  • Average speed = 60 km / h
  • Distance = 4 km

How:

\ large Speed \ hspace {0.3em} mean = \ frac {Distance \ hspace {0.3em} total \ hspace {0.3em} traveled} {Time \ hspace {0.3em} of \ hspace {0.3em} traveled}

Travel time will be the distance traveled divided by the average or average speed:

speed exercise 2

The mako shark takes 0.06 h, however, they ask us for this time in seconds.

Since 1 h = 60 min and 1 min = 60 s, we have:

speed example 2 result

Consequently, it takes 241.2 s for the mako shark to travel 4 km with an average speed of 60 km / h.

  1. A person travels a distance of 15 km in 2 hours and records their movement in different time intervals in the following table:
DistanceTimeSpeed
3 km¼ hour10 km / h
6 km½ hour10 km / h
10 km1 hour2.5 m / s
14 km1.5 hours2.5 km / h
15 km2 hours4,039 mph
  • Calculate its average speed throughout the journey.

We know that:

\ large Speed \ hspace {0.3em} mean = \ frac {Distance \ hspace {0.3em} total \ hspace {0.3em} traveled} {Time \ hspace {0.3em} of \ hspace {0.3em} traveled}

Thus:

average speed exercise

  • Determine your instantaneous speed at 30 minutes, 1 hour and 2 hours.

Instantaneous speed after 30 minutes

From the table we observe that at 30 minutes its instantaneous speed is 10 km / h.

Instant speed within 1 hour of travel

From the table we observe that at the moment its instantaneous speed is 2.5 m / s. If we transform this quantity to km / h, we obtain:

As 1 m / s = 3.6 km / h:

\ large 2,5m / s \ cdot \ left (\ frac {3.6km / h} {1m / s} \ right) = 9 \ hspace {0.2em} km / h

Its speed is 9 km / h an hour of travel.

Instantaneous speed at 2 hours

From the table we observe that at two hours its instantaneous speed is 4,039 mph. If we transform this quantity to km / h, we obtain:

As 1 mph = 1,609 km / h:

\ large 4,039mph \ cdot \ left (\ frac {1,609km / h} {1mph} \ right) = 6.5 \ hspace {0.2em} km / h

Its speed at two hours is 6.5 km / h.