Displacement & Average Velocity

[Violagirl]

Homework Statement

A car travels in a straight line at 40 km/hr for 1 h and 60 km/hr for 2 h. A) How far does it travel? B) Find the average velocity.

Homework Equations

Average velocity = Δx/Δt (change in distance/change in time)

The Attempt at a Solution

In solving for A, I got (1 h x 40 m/hr + 2 h x 60 km/hr) = 160 km/hr

For B, this is where I'm confused. I know that if I try to arrange it as suggested in the formula (160 km/hr/2-1 h), wouldn't this just leave me with the remaining distance and eliminating the unit for time? Or would that be correct? I feel like it would not be though as the formula suggests, average velocity is defined by change in distance per change in time. Any help is greatly appreciated!

 

[lewando]

The answer to A should have units of distance, not speed.

 

[Violagirl]

The answer to A should have units of distance, not speed.

Oh wow, I can't believe I missed that...Thanks a lot!

 

[PhanthomJay]

Homework Statement

A car travels in a straight line at 40 km/hr for 1 h and 60 km/hr for 2 h. A) How far does it travel? B) Find the average velocity.

Homework Equations

Average velocity = Δx/Δt (change in distance/change in time)

average velocity is total displacement divided by total time. The total distance divided by the total time is the average speed. Doesn't make any difference in this example, though.

The Attempt at a Solution

In solving for A, I got (1 h x 40 m/hr + 2 h x 60 km/hr) = 160 km/hr

right number, wrong units. You are solving for a distance.

For B, this is where I'm confused. I know that if I try to arrange it as suggested in the formula (160 km/hr/2-1 h), wouldn't this just leave me with the remaining distance and eliminating the unit for time? Or would that be correct? I feel like it would not be though as the formula suggests, average velocity is defined by change in distance per change in time. Any help is greatly appreciated!

check units! and welcome to PF!

 

[Nickie]

You are correct in your calculation for the total distance traveled, which is 160 km. However, for the average velocity, you need to use the total time of 3 hours since the car is traveling at different speeds for a total of 3 hours. So the average velocity would be 160 km/3 hours = 53.33 km/hr. This represents the constant velocity that would have resulted in the same displacement as the varying velocities over the same time period.