How Do You Calculate Average Velocity for a Two-Part Journey?

[kx250f341]

A car travels east at 73 km/h for 1.4 h. It then travels 30.0° east of north at 129 km/h for 0.5 h.
(a) What is the average speed for the trip?
87.7 km/h

(b) What is the average velocity for the trip?
Magnitude ____ km/h
Direction ____

Homework Equations

V avg= delta r/delta t
delta r= rf-ri/tf-ti

The Attempt at a Solution

64.5km-102.2km=-37.8km
.5h-1.4h=-.9h

(-37.8km)/(-.9h)=42.1 km/h

not sure how to find the direction, but I am doing my h.w. online and it tells me my answer is incorrect. Am I even going in the right direction?
Any help please?

 

[PhanthomJay]

Average velocity is total displacement divided by total time. You have to get the total displacement by vectorially adding up the 2 displacement vectors.

 

[kx250f341]

so Jay you are saying I have to find the x and y comp to find the total displacement

 

[PhanthomJay]

Yes, get the x and y components of each of the 2 displacements you have calculated, add up each separately, then get the resultant displacement magnitude and direction using pythagorus and trig. That's the total displacement, you have the time, solve for the average velocity magnitude and direction.

 

[rwisz]

To find the average velocity, we need to calculate the displacement (delta r) and the time interval (delta t) for the entire trip. The displacement for the first part of the trip (traveling east at 73 km/h for 1.4 h) can be calculated as follows:

delta r1 = (73 km/h)(1.4 h) = 102.2 km east

The displacement for the second part of the trip (traveling 30.0° east of north at 129 km/h for 0.5 h) can be calculated using trigonometry as follows:

delta r2 = (129 km/h)(cos 30°)(0.5 h) = 55.9 km north

The total displacement (delta r) for the trip is then:

delta r = 102.2 km east + 55.9 km north = 108.6 km east of north

The time interval (delta t) for the entire trip is:

delta t = 1.4 h + 0.5 h = 1.9 h

Now we can calculate the average velocity as follows:

V avg = delta r / delta t = (108.6 km east of north) / (1.9 h) = 57.2 km/h east of north

Therefore, the average velocity for the trip is 57.2 km/h east of north. This means that the car traveled at an average speed of 57.2 km/h in the direction of east of north.