Average velocity problem

In summary, the car traveled at a constant velocity of 20m/s for a certain time interval, with a 10 minute break during the trip. The average velocity for the entire trip is 15m/s. Using the formula x=vt, the total distance traveled is 36000m. The equation v(avg)=x/T can also be used to calculate the average velocity, yielding a total time of 2400 seconds for the trip.
  • #1

Homework Statement



A car takes a trip at 20m/s for a certain time interval. At any point in the trip (assuming it doesn't matter), the car takes a 10 minute break with no velocity. The average velocity for the trip is 15m/s The problem asks for the Total time and the distance travelled.


Homework Equations



x=vt
v(avg)=1/2(v+v_f)


The Attempt at a Solution



I guess I'm just confused about the rules in using the average velocity equation. This problem should be easy it seems. I have worked it out and I don't have an answer on if what I did is right or not. This is what I did.

T(total)=t(interval)+600(seconds)

x=v*t
x=v*(T-600(seconds))
x=20T-12000(meters)

2*V(avg)=v_o+v_f
=(x_o+x_f)/T=2*X/T

v(avg)=x/T Which makes me think this wasnt even necessisary since it is a general eq.

Plugging in x into the last equation you get

v(avg)*T = 20T-12000(m)
15*T=20T-12000(m)

T=2400s

Therefore x = 36000m

If this is right I would be helpful to know. If not a hint on how to use that stupid average formula would be nice.
 
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  • #2
That's the answer I get.
So unless I'm wrong also, you are correct.
 
  • #3
The answer is indeed right. The equation v(avg)=1/2(v+v_f) is only valid for constant acceleration. Somehow you used the equation to derive v(avg) = x/T, but this equation
is just the definition of v(avg). The average speed is the total distance traveled divided by the total time taken, and this is always valid. So you could have used this immediately.
 

What is average velocity and how is it calculated?

Average velocity is a measure of how fast an object is moving over a specific period of time. It is calculated by dividing the total displacement (change in position) by the total time elapsed.

What is the difference between average velocity and instantaneous velocity?

Average velocity is the overall rate of change of an object's position, while instantaneous velocity is the rate of change at a specific moment in time. Average velocity takes into account the entire period of motion, while instantaneous velocity only looks at a specific point.

Can average velocity be negative?

Yes, average velocity can be negative if the object is moving in the opposite direction of the chosen reference point. For example, if an object is moving towards the left and the reference point is to the right, the average velocity would be negative.

How is average velocity affected by changes in time and displacement?

The average velocity is directly affected by changes in both time and displacement. As time increases, the average velocity decreases if the displacement remains constant. Similarly, if the displacement increases, the average velocity will also increase.

What are some real-world applications of average velocity?

Average velocity is used in various fields such as physics, engineering, and sports. It is commonly used to calculate the speed of objects in motion, such as cars or airplanes, and to analyze the performance of athletes in sports like running or cycling.

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