Acceleration Problem: Solve for U & A

[kazuya99]

Homework Statement

I have been given a set of results to analyse, regarding acceleration of a free fall object in a piece of paper, (100g mass, 10cm card) falling through a light gate at different heights, i am having problems with working out the acceleration using formulae.
Distance from gate = 0.02m
Time = 0.163 seconds.
U = 0 i presume..or maybe not(part of my problem)
S = 0.1 (the length of the card)

Homework Equations

s = ut + 1/2at(squared)

The Attempt at a Solution

I have got 9.15 once but i think it was a coincedence.

 

[chaoseverlasting]

For the lighter objects, you have to take the air resisatance into account. The answer you got correct, would probably have been for a heavier object cause the air resistance is negligible for them.

 

[m2003]

As a scientist, it is important to approach problems with a systematic and logical approach. Let's start by identifying the variables in this problem. We have the distance (s) from the gate, time (t), initial velocity (u), and acceleration (a). The equation provided, s = ut + 1/2at^2, is known as the kinematic equation for displacement. This means that we can use this equation to solve for any of the variables, as long as we have the values for the other variables.

In this case, we have the values for s, t, and we are trying to solve for u and a. We can rearrange the equation to solve for u and a separately. For u, we can use the equation u = (s - 1/2at^2)/t. Plugging in the values we have, we get u = (0.1 - 1/2a(0.163)^2)/0.163. This gives us the initial velocity, u, as a function of acceleration, a.

To solve for a, we can use the equation a = 2(s - ut)/t^2. Plugging in the values we have, we get a = 2(0.1 - u(0.163))/0.163^2. Since we already have a function for u, we can substitute that into this equation and solve for a.

It is important to note that the units for all variables must be consistent. In this case, the distance is given in meters and the time is given in seconds, so the units for acceleration will be in meters per second squared (m/s^2). Also, make sure to pay attention to significant figures in your calculations.

I hope this helps in solving the problem and understanding the process. Remember to always approach problems with a clear and logical approach, and to double check your calculations and units. Good luck!