I am confused on how to derive time, and velocity.

In summary: I'm not even sure what a lot of the symbols in those problems mean.In summary, the conversation discusses a problem involving an automobile traveling on a straight road at different speeds and calculating the average velocity and speed for the entire trip. The relevant equations are mentioned, but it is important to carefully consider which ones to use. After some confusion, it is determined that the average velocity for the trip is 40 km/h and the average speed is also 40 km/h. It is emphasized that physics involves more than just plugging numbers into equations and requires critical thinking.
  • #1
Eclair_de_XII
1,083
91

Homework Statement


"An automobile travels on a straight road for 40-km for 30 km/h. It then continues in the same direction for another 40-km at 60 km/h. (a) What is the average velocity of the car during the full 80 km trip? (Assume that it moves in the positive x direction.) (b) What is the average speed?"

##d_1=40 km##
##d_2=80 km##
##v_1=30 km/h##
##v_2=60 km/h##

Homework Equations


##v=v_0+at##
##x-x_0=v_0t+\frac{1}{2}at^2##
##v^2 = v^2_0+2a(x-x_0)##
##x-x_0=\frac{1}{2}(v_0+v)t##
##x-x_0=vt-\frac{1}{2}at^2##

The Attempt at a Solution


Basically, I am trying to solve for time, but I am getting conflicting answers. This is the method I am typically accustomed to:

##(\frac{1 h}{30 km})(40 km) = \frac{4}{3}h##

This is an entirely different result from what I get from equation four on the list.

##(40 km) - (0 km) = \frac{1}{2}(0+30km/h)t##
##80km=(t)30km/h##
##t=\frac{8}{3}h##

As a result, I cannot solve the two parts for this problem, which this book tells me, is 40 km/h for each one. Additionally, I feel the need for a confession... This was the same book I had earlier complained about not having the proper formulae. It was not that it didn't have them; it's just that I was looking in the wrong places. My professor skipped around the chapters for her curriculum. After I had dropped the class, I tried to follow that curriculum, but the formulae I needed were in the chapters she had skipped when I was still taking her class. Anyway, I don't understand why I'm getting such conflicting answers when I try to solve for time.
 
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  • #2
Eclair_de_XII said:

Homework Statement


"An automobile travels on a straight road for 40-km for 30 km/h. It then continues in the same direction for another 40-km at 60 km/h. (a) What is the average velocity of the car during the full 80 km trip? (Assume that it moves in the positive x direction.) (b) What is the average speed?"

##d_1=40 km##
##d_2=80 km##
##v_1=30 km/h##
##v_2=60 km/h##

Homework Equations


##v=v_0+at##
##x-x_0=v_0t+\frac{1}{2}at^2##
##v^2 = v^2_0+2a(x-x_0)##
##x-x_0=\frac{1}{2}(v_0+v)t##
##x-x_0=vt-\frac{1}{2}at^2##

The Attempt at a Solution


Basically, I am trying to solve for time, but I am getting conflicting answers. This is the method I am typically accustomed to:

##(\frac{1 h}{30 km})(40 km) = \frac{4}{3}h##

This is an entirely different result from what I get from equation four on the list.

##(40 km) - (0 km) = \frac{1}{2}(0+30km/h)t##
##80km=(t)30km/h##
##t=\frac{8}{3}h##

As a result, I cannot solve the two parts for this problem, which this book tells me, is 40 km/h for each one. Additionally, I feel the need for a confession... This was the same book I had earlier complained about not having the proper formulae. It was not that it didn't have them; it's just that I was looking in the wrong places. My professor skipped around the chapters for her curriculum. After I had dropped the class, I tried to follow that curriculum, but the formulae I needed were in the chapters she had skipped when I was still taking her class. Anyway, I don't understand why I'm getting such conflicting answers when I try to solve for time.
Most of your relevant equations are not suitable for this type of problem. Some of them are for accelerated motion, which is clearly not the case here.

This problem can be solved by applying the plain old equation: distance = rate * time

If you travel 20 km at 40 km/hr, it's going to take you 20 km / 40 km/hr = 1/2 hr to go that distance.

Re-read the two parts to this problem and try again. It's a lot simpler than it looks. :wink:
 
  • #3
Eclair_de_XII said:

Homework Equations


##v=v_0+at##
##x-x_0=v_0t+\frac{1}{2}at^2##
##v^2 = v^2_0+2a(x-x_0)##
##x-x_0=\frac{1}{2}(v_0+v)t##
##x-x_0=vt-\frac{1}{2}at^2##

The Attempt at a Solution


...

This is an entirely different result from what I get from equation four on the list.
Those equations, including the fourth one, are for constant acceleration.

Physics is about much more than simply picking out equations which might happen to have the relevant quantities in them.
 
  • #4
SteamKing said:
Re-read the two parts to this problem and try again. It's a lot simpler than it looks. :wink:

I would figure otherwise, that I would average the two speeds together to get 45 mph; but the book states that it's 40 mph. It just doesn't make any sense.

SammyS said:
Physics is about much more than simply picking out equations which might happen to have the relevant quantities in them.

Yeah, no kidding. You actually have to think about which equations to use, how to use them, and whether you use them at all. It's not simply just plugging in numbers into the appropriate equations, like chemistry was for me.
 
  • #5
Wait, I think I just figured it out!

##\frac{1hr}{30km}(40km) = \frac{4}{3}hr##
##\frac{1hr}{60km}(40km) = \frac{2}{3}hr##
##\frac{4}{3}hr+\frac{2}{3}hr=2hr##
##(40km)+(40km)=80km##
##\frac{80km}{2hr}=40\frac{km}{hr}##

I'll try working on those online problems someone took the liberty of linking me to; that is, if I'm able to find some simple problems. The ones on the front page are much too complicated for me, I think.
 

Related to I am confused on how to derive time, and velocity.

1. How do you derive time?

Time is derived by measuring the duration of an event or the interval between two events. It is typically measured in seconds, minutes, hours, or days using a clock or other timekeeping device. Time can also be derived mathematically by dividing the distance traveled by the velocity of an object.

2. What is the equation for deriving time?

The equation for deriving time is t = d/v, where t is time, d is distance, and v is velocity. This equation is derived from the formula for velocity, v = d/t, by rearranging to solve for time.

3. How do you derive velocity?

Velocity is derived by dividing the distance traveled by the time it took to travel that distance. It is a measure of an object's speed and direction of motion. Velocity can also be derived mathematically by multiplying an object's acceleration by the time it has been accelerating.

4. What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement of an object divided by the total time taken to travel that distance. It gives an overall measure of an object's speed and direction over a period of time. Instantaneous velocity, on the other hand, is the velocity of an object at a specific moment in time. It is calculated by taking the derivative of an object's position with respect to time.

5. How are time and velocity related?

Time and velocity are directly related. As an object moves faster, time passes more quickly. This is known as time dilation and is described by Einstein's theory of relativity. Additionally, the rate of change of an object's position over time is its velocity, so time is required to determine an object's velocity.

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