How to Calculate Average Velocity with Displacement & Speed?

• Eunes
In summary, the problem involves a car traveling in different directions at different speeds and asks for either the average velocity or average speed over the entire trip. Average velocity takes into account the direction of travel, while average speed only considers the total distance traveled.
Eunes

Homework Statement

A car travels 14.6 km west at a speed of 40 km/h, then travels 12.0 km south at a speed of 50 km/h and finally travels 19.0 km east at a speed of 45 km/h. What is the magnitude of the average velocity for the car over the entire trip?

Homework Equations

3 kinematics equations?

The Attempt at a Solution

Not sure where to start., or where to go from there.

A car travels 15.6 km west at a speed of 40 km/h, then travels 11.4 km south at a speed of 50 km/h and finally travels 11.3 km east at a speed of 45 km/h. What is the average speed for the car over the entire trip?

It's the same thing, EXCEPT it is asking for average speed, not the average velocity as in the original question.

Regarding how to begin these types of problems:
It is useful to list all known variables, and all possible equations; this allows you to analyze the environment.

Regarding the first question:
Consider that velocity is a vector: it possesses a direction and a magnitude; consider the influence of this condition upon your answer for average velocity.

Consider that the velocity is equal to the ratio of distance traveled per unit of time: therefore, the average velocity is equal to the ratio of distance traveled per unit of time.

v(avg) = Δx(vector)/Δt​

Notice that you may not need to use kinematics equations, as you are implicitly given the times for each velocity through the implications of the ratio km/h and the units km.

Regarding the second question:
Consider that speed is a scalar and not a vector.

Eunes said:

A car travels 15.6 km west at a speed of 40 km/h, then travels 11.4 km south at a speed of 50 km/h and finally travels 11.3 km east at a speed of 45 km/h. What is the average speed for the car over the entire trip?

It's the same thing, EXCEPT it is asking for average speed, not the average velocity as in the original question.
The speed calculation involves the actual distance the wheels travelled. So if a car headed 10 km E then returned along the same road to its starting point, its distance traveled would be 20 km. Divide this by total time to calculate the average speed.

In contrast, velocity is a vector, and for average velocity you look at only where the vehicle started and where it ended up---determine the vector representing the difference between these two points, then divide by the total time of travel. So, for example, where the car returns to its starting point, the displacement is 0 km, making average velocity also 0 m/s.

To calculate average velocity, we can use the equation v = Δx/Δt, where v is the average velocity, Δx is the change in displacement, and Δt is the change in time. In this case, we have three separate displacements and speeds, so we will need to calculate the average velocity for each segment and then find the overall average velocity.

Segment 1: The car travels 14.6 km west at a speed of 40 km/h. We can use the formula v = Δx/Δt to find the average velocity for this segment. Δx = 14.6 km west and Δt = (14.6 km)/(40 km/h) = 0.365 hours. Plugging these values into the formula, we get v = (14.6 km)/(0.365 hours) = 40 km/h. So the average velocity for this segment is 40 km/h west.

Segment 2: The car travels 12.0 km south at a speed of 50 km/h. Again, we can use the formula v = Δx/Δt to find the average velocity for this segment. Δx = 12.0 km south and Δt = (12.0 km)/(50 km/h) = 0.24 hours. Plugging these values into the formula, we get v = (12.0 km)/(0.24 hours) = 50 km/h. So the average velocity for this segment is 50 km/h south.

Segment 3: The car travels 19.0 km east at a speed of 45 km/h. Using the same formula, we get v = (19.0 km)/(0.422 hours) = 45 km/h. So the average velocity for this segment is 45 km/h east.

To find the overall average velocity, we can use the formula v = (v1 + v2 + v3)/3, where v1, v2, and v3 are the average velocities for each segment. Plugging in the values we found, we get v = (40 km/h + 50 km/h + 45 km/h)/3 = 45 km/h. So the magnitude of the average velocity for the entire trip is 45 km/h. This means that if the car traveled at a constant speed of 45 km/h, it would cover the same distance and direction as it did in the

1. What is the formula for calculating average velocity with displacement and speed?

The formula for average velocity is displacement divided by time. So, the full equation is:
Average Velocity = Displacement / Time.

2. How do you calculate displacement?

Displacement is the change in position or the distance an object has traveled in a specific direction. It can be calculated by subtracting the initial position from the final position.

3. Can average velocity be negative?

Yes, average velocity can be negative if the object is moving in the opposite direction of the positive direction. For example, if an object moves from point A to point B in a negative direction, the average velocity would be negative.

4. What is the difference between average velocity and average speed?

Average velocity takes into account the direction of motion, while average speed only considers the magnitude of motion. Average speed is calculated by dividing the total distance traveled by the total time taken.

5. How does the average velocity formula relate to the slope of a graph?

The average velocity formula is similar to the slope formula (rise over run) in mathematics. In a distance vs. time graph, the slope of the line represents the average velocity of the object. The steeper the slope, the greater the average velocity.

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