V(t) = At + Bt, where t is in seconds, v is in meters per...

v(t) = At + Bt, where t is in seconds, v is in meters per second, A = 1.09 m/s², and B = -0.69 m/s³. ? 50% Part (a) What is the acceleration, in meters per second squared, of the particle at time $t_0$ = 1.0 s? a($t_0$) = m/s² ? 50% Part (b) What is the displacement, in meters, of the particle between times $t_0$ = 1.0 s and $t_1$ = 3.0 s?

Transcript

00:02 All right, looks like you may have a question about calculus -based physics and how it applies to acceleration, velocity, and displacement.

00:13 I'm not sure what the equation was to start with because you didn't include that on your screen capture.

00:21 You just had the question.

00:23 So i'm just going to walk through the fundamentals of calculus -based physics when the acceleration is.

00:32 Known, whatever that function might be.

00:35 So i made up a basic acceleration function, a at any given time, a at t equals three times t.

00:44 So all we need to do there is plug in a time and it will tell us what the acceleration is.

00:50 Now, what's unique about this is that unlike in algebra -based physics, we didn't get into where the force was varying.

01:00 Here, a at t equals 3t means that at any given moment, the force is changing, so we can find out that acceleration based on plugging in whatever t might be.

01:16 The nice thing with calculus -based physics is that we can make predictions about what are the other functions based on velocity and position.

01:26 So we have to use what we call integral.

01:28 That's what that fancy s looking thing is on the front here.

01:33 So the integration of acceleration is equal to the velocity time function, which is 3 half t squared.

01:44 I assume that you're familiar with integration if this is being introduced to you...

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