Ticker-Tape Cart, moving down ramp Experient, determine acceleration w/o graphs

[hoho1]

I have just done this experiment where i have a cart roll down a ramp and a ticker tape timer does its ticks on a tape atached to the cart.
already i can make a postion (or displacement from a dot of reference)- time table. for 1.0 second going down the ramp
i all ready have finished the questions and already know the carts moving with uniform acceleration. i have created position-time, velocity-time and acceleration-time graphs as well.

the question is "graphing is suggested for determining the acceleration. however, it is possible to apply the defining equation for average acceleration to determine the acceleration of the moving object... describe how you would do this, including the assumption(s) that you must make to solve the problem. (hint: how would you obtain a fairly accurate vale of final velocity?)"

Homework Equations

∆v =∆d/∆t a=∆v/∆d a=(v_f-v_i)/∆t

The Attempt at a Solution

because i can only use infomation not obtained through graphing i have that position-time table [at 0.0m, 0.0s; 1.85m, 0.2s; 5.0m,0.4s; 9.10m,0.6s; 14.1m, 0.8s; 20.0m,1.0s] and knowlegde its a constant acceleration problem. i chose a 0.0m marker at the first clear dot on the ticker tape, so where i choose it doesn't affect the results.

my try was intial velocity was 0m/s, change in time 1.0s, displacement 20.0cm

∆d=(v_i ) ∆t+(a ∆t²)/2 which becuase of the above ∆d=(a(∆t)²)/2
then a=(2∆d)/(∆t²) but this results in the value of 40m/s²? this can't be right because my value that i got from the graphs gave me 24m/s².

help needed for another way to solve this or find final velocity

oh yeah if no one knows ∆ is change in just in case, d is displacement, v is velocity, a is acceleration, t is time in s

 

[Delphi51]

Welcome to PF, hoho.
The problem here is that there is error in the measurements - rounding the distance to the nearest 1 mm makes quite a difference when you take the difference between two such values. You need to average over many dots. The usual way to do this is with a table like this:

These are not your numbers - just an example from another tickertape experiment. Notice that you get wildly different numbers in the acceleration column, but averaging that last column will provide a reasonable value for the acceleration. I see I made a mistake on the last number - should be -300, not 300.

 

[kerimek]

Hello, thank you for sharing your experiment and results. Your approach to determining the acceleration without using graphs is valid. However, the value you obtained for acceleration (40m/s2) is incorrect. This could be due to a miscalculation or an error in the experiment.

One way to obtain a more accurate value for final velocity is to use the ticker tape timer to measure the time between two consecutive dots on the tape. This will give you the time interval (∆t) between the two positions (∆d). Then, using the equation ∆v = ∆d/∆t, you can calculate the average velocity between those two positions. Repeat this process for several pairs of consecutive dots and take the average of the calculated velocities. This will give you a more accurate value for the final velocity of the cart at the end of the ramp.

Once you have the final velocity, you can use the equation a = (vf - vi)/∆t to calculate the acceleration. Make sure to use the same reference point for your initial velocity (vi) as you did for your displacement (∆d). This will ensure that your calculation is accurate.

In terms of assumptions, you are assuming that the cart is moving with a constant acceleration throughout the experiment. This may not be entirely accurate, as there may be external factors (such as friction) that could affect the acceleration of the cart. However, for the purposes of this experiment, it is a reasonable assumption to make.

I hope this helps you in your experiment and understanding of acceleration. Keep up the good work as a scientist!