How much time and distance is covered on a trip with varying speeds?

In summary: So, for the summary:In summary, a person takes a trip with a constant speed of 91.0 km/h, except for a 22-minute rest stop. The average speed for the entire trip is 64 km/h. Using the equations of driving speed and average speed, we can deduce the total distance traveled (D) and the time spent driving (T). The two equations are 91 = D/T and 64 = D/(T+22/60), and solving for D and T will give us the distance traveled and time spent on the trip, respectively.
  • #1
balling12
47
0

Homework Statement


A person takes a trip, driving with a constant speed of 91.0 km/h except for a 22.0 min rest stop. If the person's average speed is 62.4 km/h, how much time is spent on the trip and how far does the person travel?



Homework Equations





The Attempt at a Solution


not sure how to begin
 
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  • #2


You haven't put anything under the relevant equations. The problem asks you to deduce distance traveled and time spent based on an average speed. What is the definition of average speed?
 
  • #3


Let T be the total time that he drives (not including the rest stop), and D the total distance that he travels. You know that D/T = 91 km/h. That's one equation.

What is the average speed in terms of D and T? This will be your second equation.

You can solve these two equations for D.
 
  • #4


average speed= total distance/total time
 
  • #5


Right, and how does the total time relate to the time that he drives (which is T using dx's notation)?
 
  • #6


T-22 minutes?
 
  • #7


balling12 said:
T-22 minutes?

Why subtraction? Are you saying that the total time for the trip is LESS than the time spent driving?

If I spend T minutes driving *and* 22 minutes sitting at a rest stop, what is the total time I spend on the trip?
 
  • #8


ok so it would be the total time(T)+22. sorry i got that confused. But i am still unsure were to go from there?
 
  • #9


balling12 said:
ok so it would be the total time(T)+22. sorry i got that confused. But i am still unsure were to go from there?

Remember that you have two equations and two unknowns. The unknowns are:

distance traveled (D)

time spent driving (T)

The two equations are:

driving speed = 91 km/h = distance driven/time spent driving = D/T

average speed (by *definition*) = 64 km/h = distance traveled / TOTAL time = D/(T+22)

Two equations, two unknowns. This means that you can get a unique solution for both D and T.
 
  • #10


Here are the equations more cleanly:

91 = D/T

64 = D/(T+22)
 
  • #11


It's better to write 22 minutes as 22/60 hours to keep the units consistent. Then you will get the answers for D and T in kilometers and hours respectively.
 

Related to How much time and distance is covered on a trip with varying speeds?

1. What is speed in physics?

Speed in physics is defined as the rate at which an object covers a certain distance in a specific amount of time. It is a basic concept in kinematics and is calculated by dividing the distance traveled by the time it took to travel that distance.

2. How is speed different from velocity?

Speed and velocity are often used interchangeably, but they actually have different meanings in physics. While speed is the rate of change of distance, velocity is the rate of change of displacement. Velocity also takes into account the direction of motion, while speed does not.

3. How is speed calculated?

Speed is calculated by dividing the distance traveled by the time it took to travel that distance. The formula for speed is: speed = distance/time. The SI unit for speed is meters per second (m/s).

4. Can an object have a constant speed and changing velocity?

Yes, an object can have a constant speed but changing velocity. This is because velocity takes into account both the magnitude and direction of motion, so even if the object is moving at a constant speed, if it changes direction, its velocity will also change.

5. How does speed relate to other concepts in physics?

Speed is related to other concepts in physics, such as acceleration and displacement. Acceleration is the rate of change of velocity, and displacement is the change in an object's position. These concepts are closely related and often used together in calculations involving motion.

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