Calculating Distance Traveled Using Velocity Function and Integration

[FaraDazed]

Homework Statement

if $v = 8t - 3t^2$ and the body is at P

find where the body is from P when t=3

The Attempt at a Solution

I am very new to calculus and have just been taught basics of differentiation and integration.

I know that when you integrate there is an arbitrary constant so I have go this far (below).

$∫ ( v = 8t - 3t^2 ) dt = 4t^2 - t^3 + C$

I am not sure what to do with the constant, is it ignored and thus the answer is as below

$s = 4t^2 - t^3$
$s = (4 \times 9) - 27$
$s = 36 - 27$
$s = 9$metres ?

Or do I have to do something with the constant?

 

[rock.freak667]

Normally at t=0, s=0 and v=0. So your constant C will work out to be 0. So what you did is correct.

 

[Ray Vickson]

Homework Statement

if $v = 8t - 3t^2$ and the body is at P

find where the body is from P when t=3

The Attempt at a Solution

I am very new to calculus and have just been taught basics of differentiation and integration.

I know that when you integrate there is an arbitrary constant so I have go this far (below).

$∫ ( v = 8t - 3t^2 ) dt = 4t^2 - t^3 + C$

I am not sure what to do with the constant, is it ignored and thus the answer is as below

$s = 4t^2 - t^3$
$s = (4 \times 9) - 27$
$s = 36 - 27$
$s = 9$metres ?

Or do I have to do something with the constant?

The distance traveled is s(t) - s(0), from which C drops out.

RGV

 

[FaraDazed]

Normally at t=0, s=0 and v=0. So your constant C will work out to be 0. So what you did is correct.

The distance traveled is s(t) - s(0), from which C drops out.

RGV

OK thanks for the help :)