CAPA problem - Kinematics in 1 Dimension

In summary, the car had a constant acceleration of 2.10 m/s2 and traveled 29.6 m in 0.8 s. The initial velocity at t=0 was 36.16 m/s.
  • #1
ghostanime2001
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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
[tex]\Delta[/tex]x = 29.6 m
a = 2.10 m/s2
vi = ?
[tex]\Delta[/tex]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:
[tex]x_{f} = x_{i} + v_{i}\Delta t + \frac{1}{2}a(\Delta t)^{2}[/tex]

[tex]x_{f} - x_{i}= v_{i}\Delta t + \frac{1}{2}a(\Delta t)^{2}[/tex]

[tex]\Delta x= v_{i}\Delta t + \frac{1}{2}a(\Delta t)^{2}[/tex]

solving for [tex]v_{i}[/tex] gives the expression:

[tex]\frac{\Delta x - \frac{1}{2}a\Delta t^{2}}{\Delta t} = v_{i}[/tex]

substitute all the numbers:

[tex]\frac{(29.6) - \frac{1}{2}(1.2)\(0.8)^{2}}{((0.8)}[/tex]

[tex]36.52 m/s = v_{i}[/tex]

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 :(
 
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  • #2
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
Okay so is it like this then?

[tex]v_{f}=v_{i}+a\Delta t[/tex] from ti=0 to tf=4.1

[tex]36.52=v_{i}+(2.1)(4.1)[/tex]

[tex]-v_{i}=(2.1)(4.1)-36.52[/tex]

[tex]-v_{i}=-27.91[/tex]

[tex]v_{i}=27.91[/tex] m/s

Okay now?
 
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  • #4
ghostanime2001 said:
substitute all the numbers:

[tex]\frac{(29.6) - \frac{1}{2}(1.2)\(0.8)^{2}}{((0.8)}[/tex]

[tex]36.52 m/s = v_{i}[/tex]

(

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

ehild
 
  • #5
36.16?
 
  • #6
Yes, and correct the value of (v0), too.

ehild
 
  • #7
wow.. after so long finally I figured it out :( and I lost all my marks on that one question.
 
  • #8
how do I know this is the answer?
 
  • #9
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
very naaaiiiceee
 
  • #11
It traveled 29.6m in .8 seconds and then you can change that to m/s for the velocity
 

FAQ: CAPA problem - Kinematics in 1 Dimension

1. What is a CAPA problem?

A CAPA problem is a type of physics problem that involves using the principles of kinematics to solve for the motion of an object in one dimension. "CAPA" stands for "Conceptual Analysis and Problem Assessment".

2. What is kinematics?

Kinematics is a branch of physics that deals with the motion of objects without considering the forces that cause the motion. It involves analyzing the position, velocity, and acceleration of an object over time.

3. What does "1 dimension" mean in kinematics?

In kinematics, "1 dimension" refers to the fact that we are only considering motion along a single straight line. This simplifies the problem and allows us to use equations that are specific to 1-dimensional motion.

4. How do I solve a CAPA problem in kinematics?

To solve a CAPA problem in kinematics, you first need to analyze the given information and identify what is known and what is unknown. Then, you can use equations such as the kinematic equations or the formula for average velocity to solve for the unknown variable.

5. What are some common mistakes to avoid when solving a CAPA problem in kinematics?

Some common mistakes to avoid when solving a CAPA problem in kinematics include using incorrect equations, not paying attention to units, and forgetting to consider the direction of motion. It is also important to check your final answer to make sure it makes sense in the context of the problem.

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