Constant velocity and acceleration

Question

A family road trip starts out in a van traveling 50km at a velocity of 75km/hr followed by a spot of a slow traffic where they travel 10km at a velocity of 25km/hr. What is the average velocity during the trip km/hr?

2. A car moves with velocity of 60km/hr for 45min. The driver takes a 15min break at a gas station before traveling at 70km/hr for 30min. What was the average velocity of the car over the total trip in km/hr?

Answer 1

You start with the definition of average and instantaneous velocity*;

The average velocity is defined for a specific PERIOD of time. The average velocity will be equal to the change in position of an object (the van in the first problem and the car in the second) from the start until the end of that period of time.

v_average = (total change in position/total change in time)Δ

The average velocity is just that; an average over a time period It does NOT tell you how that the instantaneous velocity might have changed during that time period

In each of the two problems, you have to determine the average velocity for the trip; to do this, you have to find the total distance they travel (that is their total change in position) and the amount of time it took for the entire trip.

But to do that you have to break each trip into different parts where you have different motions, which in this case involves CONSTANT velocities (Δx=vΔt, where Δx is the change in position, v is a CONSTANT instantaneous velocity and Δt is the change in time)

In the van problem, we have two legs

1) the van travels 50 km at a constant instantaneous velocity of 75 km/hr

2) the van travels 10 km at a constant instantaneous velocity of 25 km/hr

In both legs, you have the distance traveled and you can add them up for the total distance traveled, but you don't know the time it took for each of the two legs. for each leg, you simply use the distance and velocity to find that time it took, using the formula above.

you add the total distance traveled (the total change in position) and the total time to solve for the average velocity.

for the car, there are 3 legs

1) it moves at a constant instantaneous velocity of 60km/hr for 45min.

2) it stops for 15min

3) it moves at a constant instantaneous velocity of 70km/hr for 30min.

In the case of the car, we are give the times required for each leg and the velocity but not the distances traveled during each leg, but with the formula I showed above you can solve for the distances traveled in each leg. (be careful with the time units; the time are given in minutes and not hours which the velocities are given in km/hr; my advice would be to convert the times to hours.)

*strictly speaking velocity is a vector as is position; that means the directory as well as the magnitude is needed to define it, but for the purposes of these problems, we're talking about 1 dimensional motion in the same direction.

Answer 2

Hi Margaret K.,

Average velocity is the total distance traveled divided by the time total time it took to travel that distance.

v_avg = Δd / Δt.

Δd = 50 km + 10 km = 60 km

Δt = (50 km) / (75 km/hr) + (10 km)/ (25 km/hr) = 2/3 hr + 2/5 hr = 16/5 hr

v_avg = 60 km / (16/5 hr) = 56 1/4 km/hr

See if you can do #2. And the 15 min break at the gas station is added to Δt, because he went 0 km/hr for 15 min)

I hope this helps, Joe.