A glider on an air track carries a flag of length through a stationary photogate that measures the time interval [box]td during which the flag blocks a beam of infrared light passing across the gate. The ratio vd = l(italicized)/[box]td is the average velocity of the glider over this part of its motion. Suppose the glider moves with constant acceleration. (a) Argue for or the against idea that vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate in terms of distance. (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 terms of time.

Question

A glider on an air track carries a flag of length through a stationary photogate that measures the time interval [box]td during which the flag blocks a beam of infrared light passing across the gate. The ratio vd = l(italicized)/[box]td is the average velocity of the glider over this part of its motion. Suppose the glider moves with constant acceleration. (a) Argue for or the against idea that vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate in terms of distance. (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 terms of time.

Answer 1

Assuming a constant friction force, which is reasonable, the velocity will decrease linearly with time. In such a situation, the instantaneous velocity is the velocity at the middle of the time interval.

Answer 2

I still don't get it. could you answer (a) and (b) in two parts.

Answer 3

and the flag is of length l(italicized)

Answer 4

To understand whether the average velocity vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate, we need to consider the definitions of average velocity and instantaneous velocity.

(a) In terms of distance:
Average Velocity (vd) is defined as the total distance traveled divided by the total time taken. Mathematically, it is given by vd = l/[box]td.

Instantaneous Velocity is the velocity of an object at a particular instant in time, or a specific point in its motion. It represents the object's velocity at that precise moment.

Now, when the glider is halfway through the photogate, it means that it has covered half the total distance. However, since the glider is moving with constant acceleration, its velocity is not constant. Therefore, the instantaneous velocity at the halfway point won't be the same as the average velocity over that part of its motion.

To calculate the instantaneous velocity at the halfway point, one needs additional information about the acceleration of the glider.

So, based on the given information, we cannot argue that vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate in terms of distance.

(b) In terms of time:
The same argument holds for the idea that vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate in terms of time. Since the glider's velocity is changing due to constant acceleration, the instantaneous velocity at the halfway point won't be equal to the average velocity.

In conclusion, considering both distance and time, we cannot argue that the average velocity vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate.