# Acceleration Problem: Solve for U & A

• kazuya99
In summary, the conversation discusses the difficulties in calculating acceleration for a free fall object based on given results. The equation s = ut + 1/2at^2 is mentioned, and the possibility of air resistance affecting the results is brought up. The speaker also mentions getting a possibly incorrect answer due to not accounting for air resistance.

## 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.

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.

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!

## 1. What is the equation for acceleration?

The equation for acceleration is a = (vf - vi)/t, where a represents acceleration, vf represents final velocity, vi represents initial velocity, and t represents time.

## 2. How do you solve for acceleration?

To solve for acceleration, you need to rearrange the equation a = (vf - vi)/t to isolate the acceleration variable (a). This can be done by multiplying both sides by t and then rearranging the equation to a = (vf - vi)/t. Plug in the values for vf, vi, and t to calculate the acceleration.

## 3. What is the acceleration formula for a falling object?

The acceleration formula for a falling object is a = g, where g is the acceleration due to gravity (9.8 m/s² on Earth). This means that the acceleration of a falling object is constant and does not depend on the object's mass.

## 4. How do you solve for initial velocity?

To solve for initial velocity, you can use the rearranged equation vi = vf - at. Plug in the values for vf, a, and t to calculate the initial velocity.

## 5. What units are used to measure acceleration?

Acceleration is measured in units of meters per second squared (m/s²) in the metric system and feet per second squared (ft/s²) in the imperial system.