Help understanding why v is negative but moving positively

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In summary, the conversation discusses a problem involving a car moving in the positive x direction with a given initial velocity and acceleration. The example mentions that the car's average acceleration is negative, indicating that its velocity is decreasing over time. However, the velocity itself is still positive, only the magnitude is decreasing. This is shown on a graph where the slope, or acceleration, is negative but the value of the velocity at any given point is still positive. The confusion may arise from the calculation of average velocity, where the correct formula is v_avg = (v_i + v_f)/2.
  • #1
Frankenstein19
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Homework Statement


WP_20160208_008.jpg

(This is a photocopy of the page, no real books were defiled in the process of studying :P)

Homework Equations

The Attempt at a Solution


In an example in my book, a problem reads that a car is moving in the positive x direction, the initial velocity is 15m/s and it takes 5 seconds to slow down to 5m/s. The example tells me the cars average acceleration is -2m/s^2. Then it says that in this case the acceleration is to the left, in the negative x direction evn though the velocity is pointing right. (I assume they mean instantaneous velocity) Now what I don't understand is how can the velocity be moving in the positive x direction but have a negative magnitude? If v1= 15 and vf=5, then the average v= -10. so if the signs tells us where the direction is, and this says it's negative, why is it moving in the positive x direction?
 
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  • #2
Frankenstein19 said:

Homework Statement


View attachment 95555
(This is a photocopy of the page, no real books were defiled in the process of studying :P)

Homework Equations

The Attempt at a Solution


In an example in my book, a problem reads that a car is moving in the positive x direction, the initial velocity is 15m/s and it takes 5 seconds to slow down to 5m/s. The example tells me the cars average acceleration is -2m/s^2. Then it says that in this case the acceleration is to the left, in the negative x direction evn though the velocity is pointing right. (I assume they mean instantaneous velocity) Now what I don't understand is how can the velocity be moving in the positive x direction but have a negative magnitude? If v1= 15 and vf=5, then the average v= -10. so if the signs tells us where the direction is, and this says it's negative, why is it moving in the positive x direction?
You're getting mixed up here. The car is said to be slowing down, which means that its velocity is decreasing over time. That's what the average acceleration of -2 m/s2 is telling you.

It does not mean the velocity is negative while the car is slowing, only that its magnitude is decreasing but still positive.

You're also not calculating the average velocity correctly. The formula for the average is ##v_{avg} = \frac{v_i + v_f}{2}##
 
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  • #3
The above formula of average velocity being the arithmetic mean of the initial and final velocities works only if there's constant acceleration or retardation
Otherwise
I would use average velocity=Displacement/Time
 
  • #4
Frankenstein19 said:

Homework Statement


View attachment 95555
(This is a photocopy of the page, no real books were defiled in the process of studying :P)

Homework Equations

The Attempt at a Solution


In an example in my book, a problem reads that a car is moving in the positive x direction, the initial velocity is 15m/s and it takes 5 seconds to slow down to 5m/s. The example tells me the cars average acceleration is -2m/s^2. Then it says that in this case the acceleration is to the left, in the negative x direction evn though the velocity is pointing right. (I assume they mean instantaneous velocity) Now what I don't understand is how can the velocity be moving in the positive x direction but have a negative magnitude? If v1= 15 and vf=5, then the average v= -10. so if the signs tells us where the direction is, and this says it's negative, why is it moving in the positive x direction?

If you plot a graph of velocity ##v## vs. time ##t##, then whether or not ##v## is positive or negative just depends on whether the graphed point ##(t,v)## lies above or below the ##t##-axis.

The acceleration is the slope of the graph, so if acceleration is > 0 the slope is upward (##v## increases as ##t## increases), while if acceleration is < 0 the slope is downward (##v## decreases as ##t## increases). You seem to be confused between the value on the graph at ##(t,v)## and the slope of the graph at the point ##(t,v)##.
 
  • #5
Now what I don't understand is how can the velocity be moving in the positive x direction but have a negative magnitude?

It doesn't. It has positive Velocity (its always moving in the + ve x direction), but it has negative acceleration (=deceleration in this case). It slows from +15 to +5m/S.
If v1= 15 and vf=5, then the average v= -10.

Since when has the average of 15 and 5 been -10 ?

Perhaps you mean the change in Velocity? The change is negative which tells you the acceleration is negative but both the initial and final velocities are +ve.
 

1. Why is v negative if it's moving positively?

This can be explained by the direction of the motion and the reference point. In physics, positive direction is usually defined as moving towards a certain direction, while negative direction is moving away from that direction. If v is moving in the positive direction, but away from the reference point, it will be considered negative.

2. Can v be negative and positive at the same time?

No, v can only have one value at a time. However, its value can change from negative to positive or vice versa depending on the direction of its motion.

3. How can v be negative if it's moving in a straight line?

Even if v is moving in a straight line, its direction can still be negative. This can happen if the reference point is located in the opposite direction of the motion.

4. Does the negative value of v affect its speed?

No, the negative value of v does not affect its speed. The speed of an object is determined by its magnitude, which is always positive. The negative value only indicates the direction of the motion.

5. How can I visualize v being negative but moving positively?

One way to visualize this is by imagining a car moving forward on a highway. If the car is moving in the positive direction, but away from the starting point, its velocity can be represented as negative. This is because the car is still moving forward, but in relation to the reference point, it is moving away.

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