Particle Displacement - Integration

Homework Statement

the velocity v m/s of a body moving in a straight line is given by v = 3t^2 - 4t - 4. if the body has an initial displacement of 3 m from O, find:
*a. the displacement and acceleration at any time t s;
*b. the time when the body is momentarily at rest;
*c. the distance travelled in the first three seconds.

Homework Equations

Common Integration

The Attempt at a Solution

Ok so I can do a) and b ) without any troubles. It's c I'm having a problem with. I can do it with a Velocity vs Time graph (Find the area underneath) and just use a number line. Except I can't find a relationship between time and distance. Can anyone help?

Cyosis
Homework Helper
How did you find the displacement as a function of time?

I integrated the velocity function and found a displacement equation;
d(t) = t^3 - 2t^2 -4t + 3.
Except this gives displacement, not distance. Thats why I'm stuck :(

I cant remember the first three seconds mean in high school. But just integration time from o to 3(0r maybe 2).

Cyosis
Homework Helper
What's the difference between the displacement and the distance?

I cant remember the first three seconds mean in high school. But just integration time from o to 3(0r maybe 2).
It gives -3 when the answer is 13m.

What's the difference between the displacement and the distance?
"Distance is the scalar value of how far an object has traveled regardless of direction.
Displacement is the vector value of how far an object has been displaced, meaning how far is it from where it started. "

I integrated the velocity function and found a displacement equation;
d(t) = t^3 - 2t^2 -4t + 3.
Except this gives displacement, not distance. Thats why I'm stuck :(

you can know the displacement d(0) while t=0 from the expression. and in the same way, the displacement while t=3. of course you can calculate the distance.

Distance and Displacement are different. If I sub in 3 for t in the displacement equation I get 0. Can you explain what you said with an equation?

"Distance is the scalar value of how far an object has traveled regardless of direction.
Displacement is the vector value of how far an object has been displaced, meaning how far is it from where it started. "

that's it. just minus them

Distance and Displacement are different. If I sub in 3 for t in the displacement equation I get 0. Can you explain what you said with an equation?

ok, i have figured out your problem.
if u sub in 3 into the equation, it turns out to be 0. what does it mean?
it means the O of axis.

It means that at 3 seconds the displacement of the body is 0 m from the starting point. This doesn't help me find distance.

the particle first located the position which has displacement of 3m from O. and then moved back to O. how long did it traveled?

the particle first located the position which has displacement of 3m from O. and then moved back to O. how long did it traveled?

O, if you mean the distance not the displacement of the two events, then forget it!
i always misunderstand the high school title.

by using mathematica, i drew a picture of the displacement.

Attachments

• dd.bmp
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you can know the rest point from question b), then multiple it by 2, and add the displacement of 3m. finally, you can get the answer.