Calculate Acceleration & Velocity of Motion Under Gravity

In summary: Notice that the acceleration is the limit of the velocity:x'(t) = lim(v(t+dt)-v(t))/{(t+dt)-t}In summary, the acceleration is the limit of the velocity.
  • #1
math4me
13
0
I would really appreciate some help on this please:

Distance in metres
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

Time talen to travel distance (in seconds)

0.72
1.28
1.67
1.85
2.08
2.50
2.83
3.01
3.13
3.25

What would you expect the accelartion to be and also what would you expect the velocity to be?

Mass = 0.164 Kg

Inital velocity = 0.

The experiment was letting a cylinder roll down the ramp and the data is above.

I just can't seem to calculate the acceleration and velocity could someone please help me thank you very much (much appreciated).
 
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  • #2
You know that:
[tex]x(t) = x_0 + v_0t + \frac{1}{2}at^2[/tex]
You have three variables, x0, v0 and a. You already know that x0 and v0 are zero, so that leaves you with:
[tex]x(t) = \frac{1}{2}at^2[/tex]
To find the acceleration just use one of the measurements, for example 1m and 3.25s:
[tex]1m = \frac{1}{2}a(3.25s)^2[/tex]
As for calculating the velocity, that is just:
[tex]v(t) = v_0 + at[/tex]
The value of t varies depending on when you want to find the velocity.
 
  • #3
At the last point the final velocity, so what would the acceleration be, not to clude up on the equation(s).

Thank you very much
 
  • #4
Anybody please tyty.
 
  • #5
I don't understand your questions.
 
  • #6
In a discrete set of data, acceleration will require two time intervals, since it is a second order derivative.

(note: position is zeroth order, and does not require an interval, just a point; velocity is first order, and therefore requires one time interval, that is, two points; every order of time derivative, requires that many time intervals to specify)

You have 9 time intervals, so, you have 8 meaningful accelerations. I'll give you an example:

(t,x)0 = (0.1,0.72)
(t,x)1 = (0.2,1.28)
(t,x)2 = (0.3,1.67)

This gives you three positions (three null intervals), two velocities (2 x 1 interval), and one acceleration (1 x 2 intervals). The velocity is the space interval divided by the time interval from one point to the next:

v0 = (x1 - x0)/(t1 - t0) = (1.28 - 0.72)/(0.2 - 0.1) = 5.6
v1 = (x2 - x1)/(t2 - t1) = (1.67 - 1.28)/(0.3 - 0.1) = 3.9

Notice that the velocity is changing, thus, there is an acceleration.

a0 = (v1 - v0)/(t1 - t0) = (3.9 - 5.6)/(0.2 - 0.1) = -17

There are also other ways to do it.


Notice the similarity in:

x'(t) = lim(as dt -> 0){x(t+dt)-x(t)}/{(t+dt)-t}

The discrete treatment given above is a consequence of not taking the limit.
 
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FAQ: Calculate Acceleration & Velocity of Motion Under Gravity

What is acceleration of motion under gravity?

Acceleration of motion under gravity is the rate at which an object's velocity changes due to the force of gravity. It is commonly denoted as 'g' and has a value of approximately 9.8 meters per second squared.

How do you calculate acceleration of motion under gravity?

To calculate acceleration of motion under gravity, you can use the formula a = g, where 'a' is the acceleration and 'g' is the gravitational acceleration. Alternatively, you can use the formula a = Δv/Δt, where 'Δv' is the change in velocity and 'Δt' is the change in time.

What is the difference between acceleration and velocity of motion under gravity?

Acceleration is the rate of change of velocity, while velocity is the rate of change of position. In the context of motion under gravity, acceleration is the change in velocity due to the force of gravity, while velocity is the speed and direction of the object's motion.

Can you calculate acceleration and velocity of motion under gravity for any object?

Yes, acceleration and velocity of motion under gravity can be calculated for any object. However, the value of acceleration may vary depending on the mass and shape of the object, as well as external factors such as air resistance.

How does the acceleration and velocity of motion under gravity change for objects of different masses?

The acceleration of motion under gravity is constant for all objects and does not depend on mass. However, the velocity may differ for objects of different masses due to the force of gravity being directly proportional to the mass of the object.

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