A Glider of length moves through

[AryRezvani]

Homework Statement

A glider of length moves through a stationary photogate on an air track. A photogate shown in the figure below is a device that measures the time interval Δtd during which the glider blocks a beam of infrared light passing across the photogate. The ratio vd = /Δtd is the average velocity of the glider over this part of its motion. Suppose the glider moves with constant acceleration.

(a) Argue for or against the idea that vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate in space.(b) Argue for or against the idea that vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate in time.

Homework Equations

None

The Attempt at a Solution

On (a), I'm not exactly sure how to think of this problem. What does it mean by space?

Regarding (B), I believe the instantaneous velocity is equal to the average velocity at the halfway point. This is because the velocity decreases linearly.

 

[Simon Bridge]

On (a), I'm not exactly sure how to think of this problem. What does it mean by space?

as opposed to "time" ... you know: thing thing you have lengths and volumes in. eg. "The air track and glider take up some space."

Regarding (B), I believe the instantaneous velocity is equal to the average velocity at the halfway point. This is because the velocity decreases linearly.

I think your description is missing a symbol for the length of the glider.

I think you need to first define what "instantanious velocity" means for the glider.

 

[AryRezvani]

as opposed to "time" ... you know: thing thing you have lengths and volumes in. eg. "The air track and glider take up some space."I think your description is missing a symbol for the length of the glider.

I think you need to first define what "instantanious velocity" means for the glider.

I'm sorry, I'm still confused. Could you perhaps describe the difference between space and time? (Just a short sentence or two. I don't want to waste your time)

The instantaneous velocity (the velocity of an object at a certain time) at the half point between the two laser points is equal to the average velocity of the entire flight. This is because the glider, which has a length of l, has a velocity that decreases linearly.

How's that?

 

[Simon Bridge]

I'm sorry, I'm still confused. Could you perhaps describe the difference between space and time? (Just a short sentence or two. I don't want to waste your time)

What? You are talking about one of the deep and enduring mysteries of the Universe ... in a few sentences?

For your purposes,
Time is because things happen ... time is the stuff that is made by clocks: you measure it with a standard clock like a stopwatch.

Space is because things have to have someplace to happen in. The amount of space is called the volume. You measure it with a ruler.

The other important aspect of the universe is matter - matter is the stuff that has inertia - the amount of inertia is called the mass. You measure mass with a balance.

All the question is saying is that the glider changes position.

The instantaneous velocity (the velocity of an object at a certain time) at the half point between the two laser points is equal to the average velocity of the entire flight. This is because the glider, which has a length of l, has a velocity that decreases linearly.

How's that?

No - I mean, how would you relate the concept of "instantaneous velocity" to an object normally?

But I think your answer is reasonable for all that.

 

[Nickie]

I would approach this problem by first defining the terms and variables involved. The glider's length is given as L, and it moves through a stationary photogate, which is a device that measures the time interval Δtd when the glider blocks a beam of infrared light. The ratio vd = L/Δtd is defined as the average velocity of the glider over this part of its motion. The problem states that the glider moves with constant acceleration.

(a) To answer whether vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate in space, we need to consider the definition of instantaneous velocity. Instantaneous velocity is the velocity of an object at a specific instant in time. In this case, the halfway point in space would refer to the midpoint of the photogate. However, since the glider is moving with constant acceleration, its velocity is changing continuously. Therefore, the instantaneous velocity at the midpoint of the photogate would not be equal to the average velocity over that part of its motion.

(b) For the second part, we need to consider the definition of instantaneous velocity again. This time, the halfway point in time would refer to the midpoint of the time interval Δtd. Since the glider is moving with constant acceleration, its velocity at the midpoint of the time interval would be equal to the average velocity over that part of its motion. Therefore, we can argue that vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate in time.

In conclusion, the instantaneous velocity of the glider at the midpoint of the photogate in space is not equal to the average velocity over that part of its motion, but the instantaneous velocity at the midpoint of the time interval is equal to the average velocity. This is because the glider's velocity is changing continuously due to its constant acceleration.