A glider on an air track carries a flag of length through a stationary photogate that measures the time interval td during which the flag blocks a beam of infrared light passing across the gate. The ratio vd = / 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 td during which the flag blocks a beam of infrared light passing across the gate. The ratio vd = / 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.

Could someone please help?

Answer 1

length = l(italicized)

time interval = [box]td
ratio = l(italicized)/[box]td

Answer 2

I do not have the picture and do not understand the question.

Answer 3

Sure, I'd be happy to help you with this question!

(a) To 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 distance, we need to consider the motion of the glider.

If the glider is moving with constant acceleration, it means that its velocity is changing at a constant rate. In this case, the glider's velocity at any given point in time is not necessarily equal to its average velocity over a certain distance. This is because the glider's velocity may have been increasing or decreasing throughout its motion.

Therefore, we cannot conclude that vd is equal to the instantaneous velocity of the glider when it is halfway through the photogate in terms of distance. While vd may give us an average velocity over a certain distance, it does not provide information about the glider's instantaneous velocity at any specific point.

(b) To 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, we again need to consider the glider's motion.

If the glider is moving with constant acceleration, its velocity is changing at a constant rate. In this case, the velocity of the glider at any given point in time is directly related to the time it took for the glider to travel that distance.

Let's assume that the distance the glider travels when it is halfway through the photogate is d. If the glider moves with constant acceleration, the time it takes for the glider to reach this distance is related to its velocity. Specifically, the time it takes (t) can be calculated using the equation:

d = (1/2) * acceleration * (t^2)

If we rearrange this equation to solve for t, we get:

t = sqrt(2d / acceleration)

Now, if we consider the definition of average velocity (vd = d / t), we can substitute the value of t into this equation:

vd = d / (sqrt(2d / acceleration))

Simplifying this expression, we get:

vd = sqrt(acceleration / (2d))

From this analysis, we can see that the average velocity (vd) of the glider when it is halfway through the photogate in terms of time is related to the acceleration and the distance traveled. However, it is not equal to the instantaneous velocity at that specific point, as the instantaneous velocity can vary throughout the glider's motion.

Therefore, we can argue 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.