Homework Help: Kinematics and acceleration problem

1. Jan 23, 2013

aaronfue

1. The problem statement, all variables and given/known data

A particle moves along a straight line such that its acceleration is a = (4t2-2) $\frac{m}{s^2}$, where t is in seconds. When t = 0, the particle is located 1 m to the left of the origin, and when t = 2 s, it is 20 m to the left of the origin. Determine the position of the particle when t = 4.3s.

2. Relevant equations & The attempt at a solution.

I am just stuck on this. I know I should already know how to do this but right now my mind is blank!
I know that I can get the velocity equation by integrating, but when I try to use t=2 s, and then using the equation x=xo+vot+$\frac{1}{2}$at2, I am not even close to the x=20.

2. Jan 23, 2013

tms

The kinematics equation you mention is good only for constant acceleration, but the acceleration in the problem varies with time, so you have to go back to basics. Start with the definition of acceleration: $a = dv/dt$.

3. Jan 23, 2013

haruspex

That equation is only valid for constant acceleration.

What do you get when you integrate the acceleration equation?

4. Jan 23, 2013

aaronfue

After I integrate the acceleration, I get:

v(t)= ($\frac{4}{3}$t3 - 2t) $\frac{m}{s}$

5. Jan 23, 2013

haruspex

Don't forget the constant of integration.
Then get the equation for distance as a function of time.

6. Jan 23, 2013

tms

Don't forget the constant of integration.

Then the next step is to find the displacement.

7. Jan 25, 2013

aaronfue

s(t) = $\frac{t^4}{3}$ - t2 + c1t + c2

c1 is the constant after integrating for v(t) & c2 is the constant for s(t).

Do I have to set the constants equal to the given positions and t=0 and t=2?

8. Jan 25, 2013

tms

No. You plug in the value for $t$, and then solve for the constants.

9. Jan 26, 2013

aaronfue

Ok. I plugged in the t=0, s=1 and got c2 = 1 (I think this would be -1 since the location is to the left of the origin?)

So I then plugged t=2, s= -20 and my c1 = -9.84

Finally I plugged my c1 and c2 into my s(t) equation:

s(t) = $\frac{1}{3}$t4 - t2 - 9.84t -1

And after using t=4.3, I got s = 52.16 m

Unfortunately, this is not correct. The correct answer was 50.8 m. I'm not sure where I messed up, but I'm thinking it was my rounding.

Last edited: Jan 26, 2013
10. Jan 26, 2013

aaronfue

Found my mistake!! I was subtracting my numbers from +20 and not using -20 when calculating my c1!!

I got:
s = 50.75 = 50.8 m!!

Dang!!!