Question

Can anyone help me?

An object has zero initial velocity and a constant acceleration of 32ft/sec^2

Find a formula for its velocity as a function of time.

V(t) = ft/s

Answer 1

Can we use the calculus?

Answer 2

Yes

Answer 3

Perfect. You should have these definitions for uniform acceleration.

Position: x(t)
Velocity: v(t) = (d/dt)x(t)
Acceleration: a(t) = (d/dt)v(t)

Seen them?

Answer 4

I suck at calculus, but i vaguely remember the velocity and acceleration one. It's basically a derivative and a double derivative?

Answer 5

That's good. You are remembering well.

Here's the quiz. If we can get from Velocity to Acceleration by the Derivative, how do you suppose we get the other direction, from Acceleration to Velocity?

Answer 6

Antiderivative?

Answer 7

You have it.

a(t) = 32 ft/s^2

It's a constant. Find the antiderivative of a(t).

Answer 8

32x + C?

Answer 9

That's the idea, but traditionally the variable of interest is 't', rather than 'x'.

In this collection of things related to uniform acceleration, that "C" is the initial velocity.

\(v(t) = 32t + v_{0}\) and the units are ft/sec

We are given the initial velocity in the problem statement. Substitute and you are done.

Answer 10

v(t) = 32t + 0 ft/sec?

Answer 11

Perfect. You can just discard the 0. It does us no good after we have identified it.

Excellent work!

Answer 12

Thanks so much! You helped a lot!