CAPA problem - Kinematics in 1 Dimension

[ghostanime2001]

Homework Statement

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
v_i = ?
$$\Delta$$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 :(

 

[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

 

[ghostanime2001]

Okay so is it like this then?

$$v_{f}=v_{i}+a\Delta t$$ from t_i=0 to t_f=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?

 

[ehild]

substitute all the numbers:

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

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

(

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

ehild

 

[ghostanime2001]

36.16?

 

[ehild]

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

ehild

 

[ghostanime2001]

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

 

[ghostanime2001]

how do I know this is the answer?

 

[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

 

[ghostanime2001]

very naaaiiiceee

 

[iRaid]

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