Homework Help: CAPA problem - Kinematics in 1 Dimension

1. Sep 22, 2010

ghostanime2001

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

A car accelerates at 2.10 m/s2 along a straight road. It passes two marks that are 29.6 m apart at times t=4.10 s and t=4.90 s. What was the car's velocity at t=0?

I'm assuming the car has constant acceleration of 2.10 m/s2

Given
$$\Delta$$x = 29.6 m
a = 2.10 m/s2
vi = ?
$$\Delta$$t = ? (I was thinking it might be 0.8 s because of 4.9 - 4.1 s )

The equation I think I should use is:
$$x_{f} = x_{i} + v_{i}\Delta t + \frac{1}{2}a(\Delta t)^{2}$$

$$x_{f} - x_{i}= v_{i}\Delta t + \frac{1}{2}a(\Delta t)^{2}$$

$$\Delta x= v_{i}\Delta t + \frac{1}{2}a(\Delta t)^{2}$$

solving for $$v_{i}$$ gives the expression:

$$\frac{\Delta x - \frac{1}{2}a\Delta t^{2}}{\Delta t} = v_{i}$$

substitute all the numbers:

$$\frac{(29.6) - \frac{1}{2}(1.2)\(0.8)^{2}}{((0.8)}$$

$$36.52 m/s = v_{i}$$

Am I right or wrong with this answer? Also, I couldn't check to make sure if its right or wrong because I kept on thinking the initial velocity should be zero and i held on to that and kept on asnwering that on CAPA and so as a result, I used up all of my tries :(

Last edited: Sep 23, 2010
2. Sep 23, 2010

ehild

That vi is the velocity at the first mark, at 4.1 s, but the problem asks v(0) the velocity at t=0.

ehild

3. Sep 23, 2010

ghostanime2001

Okay so is it like this then?

$$v_{f}=v_{i}+a\Delta t$$ from ti=0 to tf=4.1

$$36.52=v_{i}+(2.1)(4.1)$$

$$-v_{i}=(2.1)(4.1)-36.52$$

$$-v_{i}=-27.91$$

$$v_{i}=27.91$$ m/s

Okay now?

Last edited: Sep 23, 2010
4. Sep 23, 2010

ehild

The acceleration is 2.1 m/s^2. Correct your result.

ehild

5. Sep 23, 2010

ghostanime2001

36.16?

6. Sep 23, 2010

ehild

Yes, and correct the value of (v0), too.

ehild

7. Sep 23, 2010

ghostanime2001

wow.. after so long finally I figured it out :( and I lost all my marks on that one question.

8. Sep 23, 2010

ghostanime2001

how do I know this is the answer?

9. Sep 23, 2010

ehild

How do you did not know? You knew al the necessary background, all the equations, just to had to plug in the proper data without mistyping them.

ehild

10. Sep 23, 2010

ghostanime2001

very naaaiiiceee

11. Sep 23, 2010

iRaid

It traveled 29.6m in .8 seconds and then you can change that to m/s for the velocity