How do u work out a force-acceleration graph from a velocity-time graph?

Answer 1

Hi,

I would love to know the context of this question and what you are to intrepet from the force vs acceleration graph.

There are four arrangements for this problem
Constant force & constant mass
Constant force & variable mass
Variable force & constant mass
Variable force & variable mass

I am going to assume that this is a constant mass problem so this leavs only the two cases constant force and variable force.

If the force is constant then the accelreation will also be constant, using Newton's 2nd law F=ma shows that. Therefore the velocity-time graph wll be a straight line and the slope will be the acceleration.

If the mass and force are constant then the force-acceleration graph will be a single point with force = mass * acceleration and the point will be (mass * acceleration, acceleration).

If the force is not constant the velocity-time graph will not be a straight line. You will need to extract two things from that graph, the acceleration and the force. To get at these you will have to break it up into loads of sections such that the graph of each section approximates a stragiht line, to calculate the integral and the derivative. The derivative will be approximated as the slope at a point and the integral as the area under the curve in a little vertical strip. The narrowerer the strips the more accurate your calculations and final graph will be.

This will be much easier if your Vel-time graph passes through 0 and I am assuming that it does.

Divide your time axis into strips all the same width call the x values of these strips t0, t1, t2, t3, t4...etc and make a table of values. Find the corresponding velocity values for the t values and call them v0, v1, v2, ... etc. (t0, v0) should be (0, 0).

Calculate the acceleration value for the middle of each strip by getting the slope of the curve in the middle of the strip. The slope of the first strip is (v1 - v0)/(t1 - t0) call this a1 the slope of the 2nd strip is (v2 - v1)/(t2 - t1) call this a2, continue until all the accelerations have been calculated.

Calculate the distance traveled in each strip, this is the area of each strip d1 = v0 * (t1 - t0) + 0.5*(v1 - v0)*(t1 - t0)
d2 = v1 * (t2 - t1) + 0.5*(v2 - v1)*(t2 - t1)
.... etc

Now we want to calculate the kinetic energy at the midpoint of each strip. KE= 0.5*m*v^2 where m is the mass, if you do not know the mass just use 1kg but remember that the scales of your new graph will be relative values not absolute values.
k1 = 0.5 * m * ((v0 + v1)/2)^2, here we are finding the average of the veleocity at the edges of the strip.

k2 = 0.5 * m * ((v1 + v2)/2)^2

k3.... etc

Now we are going to appeal to the theorem of conservation of energy, where the work done is = to the change of kinetic energy. The work done is = the net force * distance in the direction of the force. Therefore F = delta KE/delta distance

F1 = k1/d1, F2 = k2/d2, .... etc

Now plot Fvalues on y axis versus A values on the x axis and you have force-acceleration graph made up from the points (f1, a1), (f2, a2), (f3, a3).... etc.

If you have Excel job can be calculated very quickly.

After writing all of the above I have just realised that if you plotted m*a versus a you would get the same result in a amall fraction of the time!

Hope this helps, please let me know how you get on.

Peter

Answer 2

From the velocity-time graph find the velocities at 0.5s and 1.5 s.

The difference between the velocities is the acceleration at the time of 1s.

Similarly, find the velocities from the graph for 1.5 s and 2.5 s. The difference is the acceleration at 2s.

Find for 3s, 4s, etc, till you get the accelerations for the entire time-length.

Mark the accelerations found in the x axis.

For the accelerations found, calculate the force by multiplying it by mass and plot the forces.

If the velocity time graph is a straight line, then all the accelerations found will be the same and hence there is only one value for acceleration. Force is mass times the acceleration and hence you can plot only a single point in the force acceleration graph.

Answer 3

It is not possible dude. You can only find work done, which is the area under the graph.. Coz Work done = Force x displacement even if you get work done.. it is not related to velocity and acceleration. Unless you have the mass of the object, you cannot find the object's acceleration at a specific time.

Answer 4

Find the slope of the velocity - time graph and that will be acceleration. a = dv/dt.

Force = mxa = mass x acceleration.

If acceleration is constant, force will be constant. If a varies, F too will vary since mass is constant.

Answer 5

derivative of velocity and time i.e. dv/dt gives the acceleration