## What Is The Most Economical Driving Speed

While the **most economical driving speed changes with every vehicle**, the general consensus is that **it is around 50 mph **. There are a few other things you can do to maximise efficiency, however. First, **try to maintain a constant speed**, this will make your engine run as efficiently as possible – use cruise control on flats if you have it. Second, **drive at the highest possible gear within the speed limit**, this again helps your engine run as economically as possible. Other tips include **turning off AC and having as little weight in your car as you can**.

## Average Velocity: A Graphical Interpretation

Average velocity is defined as the change in position over the time of travel.

learning objectives

- Contrast speed and velocity in physics

In everyday usage, the terms speed and velocity are used interchangeably. In physics, however, they are distinct quantities. Speed is a scalar quantity and has only magnitude. Velocity, on the other hand, is a vector quantity and so has both magnitude and direction. This distinction becomes more apparent when we calculate average speed and velocity.

Average speed is calculated as the distance traveled over the total time of travel. In contrast, average velocity is defined as the change in *position* over the total time of travel.

**Average Velocity**: The kinematic formula for calculating average velocity is the change in position over the time of travel.

The SI unit for velocity is meters per second, or m/s, but many other units are commonly used. Suppose, for example, an airplane passenger took five seconds to move -4 m . His average velocity would be:

The minus sign indicates that the average velocity is also toward the rear of the plane.

The average velocity of an object does not tell us anything about what happens to it between the starting point and ending point, however. For example, we cannot tell from average velocity whether the airplane passenger stops momentarily or backs up before he gets to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals.

## Instananeous Velocity: A Graphical Interpretation

Instantaneous velocity is the velocity of an object at a single point in time and space as calculated by the slope of the tangent line.

learning objectives

- Differentiate instantaneous velocity from other ways of determining velocity

Typically, motion is not with constant velocity nor speed. While driving in a car, for example, we continuously speed up and slow down. A graphical representation of our motion in terms of distance vs. time, therefore, would be more variable or curvy rather than a straight line, indicating motion with a constant velocity as shown below.

**Motion with Changing Velocity**: Motion is often observed with changing velocity. This would result in a curvy line when graphed with distance over time.

To calculate the speed of an object from a graph representing constant velocity, all that is needed is to find the slope of the line this would indicate the change in distance over the change in time. However, changing velocity it is not as straightforward.

**Determining instantaneous velocity**: The velocity at any given moment is dened as the slope of the tangent line through the relevant point on the graph

**Instantaneous Velocity, Acceleration, Jerk, Slopes, Graphs vs. Time**: This is how kinematics begins.

In calculus, finding the slope of curve \ at \x=x0 is equivalent to finding the first derivative:

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## What Is Average Speed

*Average speed* is calculated by dividing the total distance that something has traveled by the total amount of time it took it to travel that distance.

*Speed* is how fast something is going at a particular moment.* Average speed *measures the averagerate of speed over the extent of a trip.* Average speed* is usually applied to vehicles like cars, trains, and airplanes. It is often measured in miles per hour or kilometers per hour .

*Average speed *is used in all kinds of fields, including physics, astronomy, and transportation.

## Formula Of Average Speed

The formula for average speed is found by calculating the ratio of the total distance traveled by the body to the time taken to cover that distance.

The average speed equation is articulated as:

Total Distance traveled/Total Time taken

Equation is the formula for an average speed of an object moving at a varying speed.

**Read Also: What Does Fg Mean In Physics **

## Whats The Difference Between Mph And Kph

Kilometers per hour has an abbreviation of kph and it refers to the number of kilometers a given object traveled in one hour. Conversely, miles per hour has an abbreviation of mph and it refers to the number of miles a given object traveled in one hour. Both are units of measurements used for speed.

If you want to convert an mph value to a kph value, take the mph value and multiply this by 1.61. On the contrary, if you want to convert a kph value to an mph value, take the kph value and multiply this by 0.61. **This is because:**

1 mile = 1.61 kilometers, and 1 kilometer = 0.061 miles

You can breakdown both mph and kph into meters per second and feet per second. For kph, all you have to do is multiply the total speed by 1,000 then divide the value you get by 3,600. For mph, all you have to do is multiply the total speed by 5,280 then divide the value you get by 3,600.

The main difference between these two units of measurement is one is from the metric system while the other is from the US customary system.

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The everyday concept of speed arises when we consider how quick or slow a body moves. Somehow we relate the displacement of the body with the time spent in such displacement. In this section, we are going to define what is meant in physics by average speed and its difference with average velocity.

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## Problems Related To Both Average Speed And Average Velocity

1. A car travels along a straight road to the east for 120 meters in 5 seconds, then goes west for 60 meters in 1 second. Determine average speed and average velocity.

Solution:

Distance = 120 meters + 60 meters = 180 meters

Displacement = 120 meters 60 meters = 60 meters, to east.

Time elapsed = 5 seconds + 1 second = 6 seconds.

Average speed = Distance / time elapsed = 180 meters / 6 seconds = 30 meters/second.

Average velocity = Displacement / time elapsed = 60 meters / 6 seconds = 10 meters/second.

2. A runner is running around a rectangle track with length = 50 meters and width = 20 meters. He travels around the rectangle track twice, finally running back to the starting point. If the total time he takes to run around the track is 100 seconds, determine average speed and average velocity.

Solution:

The circumference of the rectangle, which is the distance travelled in one round = 2 + 2 = 100 meters + 40 meters = 140 meters.

When a runner runs around the rectangle twice = 2 = 280 meters.

Distance = 280 meter

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## Average Speed Solved Examples

**Problem 1: **A runner sprints at a track meet. He completes a 1000-meter lap in 1 minute 30 sec. After the finish, he is at the starting point. Calculate the average speed of the runner during this lap?**Answer:**

Total distance covered by the runner = 1000 meters

Total time taken =1minute 30 sec

= 90 secSo, applying the formula for the average speedwe have,

1000/90

11.1 m/s

**Problem 2**: A car travels at a speed of 40 km/hr for 2 hours and then decides to slow down to 30 km/hr for the next 2 hours. What is the average speed?**Answer:**D1 = 40 * 2 = 80 miles

D2 = 30 * 2 = 60 miles

Total distance D= D1+D2

D = 80 + 60

Total Distance travelled/Total Time taken

= 140/4

**Read more:**Average velocity

**See the video below, to have a clear idea about average speed, average speed formula, and average velocity.**

Hope you learned the average speed definition, average speed formula, how to calculate average speed along with examples. Stay tuned with BYJUS to know more.

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## Solved Examples On Average Speed

1. A train travels at a speed of 300 km/hr for 2 hours and then slows down to 220 km/hr for the next 2 hours. What is the average speed of the train?

Solution: Distance covered in the first 2 hours, D1 = 300 * 2 = 600 miles

Distance covered in the next 2 hours, D2 = 220 * 2 = 440 miles

Total distance covered, D= D1 + D2

D = 600 + 440 = 1040 miles

Total time taken = 4 hours

Thus, the average speed of the train = \

= 1040/4 = 260 m/s

2. A particle moves with a speed of 4m/s for 20s. It again moves with a speed of 6m/s for another 20s and finally moves with a speed of 8m/s for next 20s. Calculate the average speed of the particle?

Solution: Distance= speed x time

Distance travelled in first 20s, D1 = 20s × 4 m

= 80 m

Distance travelled in next 20s, D2 = 20 × 6 m

= 120 m

Distance travelled in the last 20s, D3 = 20 × 8 m

=100 m

Total distance travelled by particle, D = 80 + 120 + 160 m

= 360 ms

Total time taken, T = 20×3 = 60s

Therefore, the average speed, S = D/T

= 360/60 m/s

= 60 m/s

3. A person goes from Point A to Point B in 10s and returns back in 8s. If the distance between A and B is 36m, find the average speed of the person.

Solution: Here total distance covered = 72m

Total time taken = 18s

Therefore, average speed = \ = 4 m/s.

## Speed Velocity Average And Instantaneous Speed And Velocity With Examples

**SPEED AND VELOCITY**

In the last sections we have learned scalar and vector concepts. Beyond the definitions of these concepts we will try to explain speed and velocity terms. As mentioned in last section distance and displacement are different terms. Distance is a scalar quantity and displacement is a vector quantity. In the same way we can categorize speed and velocity. Speed is a scalar quantity with just concerning the magnitude and velocity is a vector quantity that must consider both magnitude and direction.

**SPEED**

Speed can be defined as how fast something moves or it can be explained more scientifically as the distance covered in a unit of time. In daily life we use the first definition and say the faster object has higher speed. Speed does not show us the direction of the motion it just gives the magnitude of what distance taken in a given time. In other words it is a scalar quantity. We use a symbol** v** to show speed. Let me formulate what we talk above

*Speed=distance/time*

From the above formula we can say that speed is directly proportional to the distance and inversely proportional to the time. I think its time to talk a little bit the units of speed. Motor vehicles commonly use kilometer per hour as a unit of speed however in short distances we can use meter per second as a unit of speed. In my examples and explanations I will use m/s as a unit.

Example Calculate the speed of the car that travels 450m in 9 seconds.

**VELOCITY**

**Average Speed= /10s**

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## How To Find Average Speed

Lets slow down and start with an example. If you were to drive 200 miles in two hours, you could calculate your *average speed* by dividing the total distance by the total amount of time it took , giving an *average speed* of 100 miles per hour.

*Average speed* might seem like a basic, obvious concept, but for much of history, people didnt have much of a practical need for such a calculation . In the 1600s, physicist and astronomer Galileo Galilei tried to calculate the speed of light by measuring how long it would take a person to see a light from across a field. It didnt work , but Galileo did come up with the formula *distance/time = average speed*.

*Average speed* should not be confused with *instantaneous speed*, which measures the speed of an object at a specific instant in time. *Instantaneous speed* is a physics term. In everyday life, we just call this *speed*, which is what the speedometer in your car tells youexactly how fast youre going at that moment. *Speed* is sometimes confused with *velocity*, but they are not the same. In physics, velocity measures somethings speed relative to its direction of motion.

In practical situations, *average speed* usually comes up in the context of transportation, such as the *average speed* of a train or airplane during a trip.

## Time Velocity And Speed

- Explain the relationships between instantaneous velocity, average velocity, instantaneous speed, average speed, displacement, and time.
- Calculate velocity and speed given initial position, initial time, final position, and final time.
- Derive a graph of velocity vs. time given a graph of position vs. time.
- Interpret a graph of velocity vs. time.

There is more to motion than distance and displacement. Questions such as, How long does a foot race take? and What was the runners speed? cannot be answered without an understanding of other concepts. In this section we add definitions of time, velocity, and speed to expand our description of motion.

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## How To Calculate Average Speed

To calculate the average speed of an object, you must know the total distance an object travels and the total elapsed time of its whole journey.

The distance/speed/time triangle is handy for calculating this and two other scalar quantities :

The three parts in the triangle are set up in their correct positions mathematically:

Average speed is especially useful because it takes into account the reality of an event, rather than assuming something or someone is moving at a constant speed.

The porpoise could have started slowly, sped up, paused to play, and continued. That three-toed sloth may have stopped for a moment to catch its breath before hurrying onward. You might have to make numerous stops when walking a dog, but in all three cases, you can easily calculate average speed by dividing the total distance traveled by total elapsed time.

## Question: What’s The Relationship Between Average Velocity And Average Speed

**Answer: **

Because displacement is always less than or equal to the distance travelled, the magnitude of average velocity is always less than or equal to the average speed. The formula V = D/t is used to calculate average velocity, where V equals average velocity, D equals total displacement, and t equals total time.

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## How Do You Convert Between Mph And Kph

To **convert from miles per hour to kilometres per hour**:

To **convert kilometres per hour to miles per hour**:

**A handy trick if you donât have a calculator** to hand is to use the Fibonacci sequence . Take a number, the next one in the sequence is the kilometres if the previous one was miles .