How to Calculate Average Velocity with Displacement & Speed?

[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.

 

[Eunes]

Also, please help solve this problem:

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.

 

[Ivan Karamazov]

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.

 

[NascentOxygen]

Also, please help solve this problem:

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.

 

[HalfLostAndSearching]

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