Find the position function

can someone please help me in how to go about solving this problem?

problem: A particle moves in a straight line and has acceleration 6cm/second square.Its initial speed is -2cm/second. Its initial position is given by f(0) = 9cm.

Find the position function f(x), where the input means the time.

here's what i know:

acceleration is f"(x) and speed is f'(x).

so i assume im looking for f(x).

but how do i setup the equation?

thanks!

Re: Find the position function

Re: Find the position function

Quote:

Originally Posted by

**noork85** can someone please help me in how to go about solving this problem?

problem: A particle moves in a straight line and has acceleration 6cm/second square.Its initial speed is -2cm/second. Its initial position is given by f(0) = 9cm.

Find the position function f(x), where the input means the time.

here's what i know:

acceleration is f"(x) and speed is f'(x).

so i assume im looking for f(x).

but how do i setup the equation?

thanks!

Surely you know how to go from f''(x) to f(x) at least...

Re: Find the position function

i do....this is what i came up with

f"(x)=6

f'(x)=6x+C...right?

Re: Find the position function

That's a good start. Now can you evaluate C?

Re: Find the position function

C is a constant...how does it relate to speed?

Re: Find the position function

you have the initial value f'(0) = -2

Re: Find the position function

f"(x)=6

f'(x)=6x+c

f'(x)=6x-2

f'(x)=3x^2-2x+D f(0)=9

f(x)=3x^2-2x+9

???

Re: Find the position function

Looks good. Of course, you can only assume that those constant values are the same as the values given because they are the initial values. If you had been given values at any other point in time, you would have had to substitute the points in and solve for the constant.