Solving for Acceleration in a Simple Kinematics Problem

[princesssuckz]

acceleration problem (HELP!:(()

Homework Statement

A vehicle accelerates to 14 m/s after being stopped at a red light. The vehicle covers 26 m to reach its final velocity. How fast was it accelerating?


HOW DO I EVEN SOLVE THIS? WHAT EQUATION AM I GONNA USE?! PLEASE HELP.:(

 

[vela]

What equations do you have?

 

[princesssuckz]

What equations do you have?

umm.. acceleration is equal to displacement over time squared.

 

[vela]

I'm afraid you're going to have to do better than that. Look in your textbook for equations for constant acceleration. Those are the ones you want to choose from.

 

[princesssuckz]

I'm afraid you're going to have to do better than that. Look in your textbook for equations for constant acceleration. Those are the ones you want to choose from.

well the only equation here related to acceleration is a=v-v_o/delta t

 

[I like Serena]

Welcome to PF, your highness princesssuckz!

Try:
$$v_f^2 = v_i^2 + 2 a \Delta x$$
Can you make sense of this formula?

 

[princesssuckz]

Welcome to PF, your highness princesssuckz!

Try:
$$v_f^2 = v_i^2 + 2 a \Delta x$$
Can you make sense of this formula?

no not really. we haven't discussed this in class yet. the teacher sort of just threw it at us.

 

[I like Serena]

no not really. we haven't discussed this in class yet. the teacher sort of just threw it at us.

Ah, well, what about this formula?
$$x=x_o + v_o t + {1 \over 2} a t^2$$

 

[princesssuckz]

Ah, well, what about this formula?
$$x=x_o + v_o t + {1 \over 2} a t^2$$

i don't get it. why is there an x?

 

[I like Serena]

i don't get it. why is there an x?

Because the problem statement says: "The vehicle covers 26 m".
This is "x".

 

[princesssuckz]

oh now i get it. i feel really stupid.

 

[I like Serena]

oh now i get it. i feel really stupid.

Uhh?

So you solved the problem?

 

[princesssuckz]

sorry. i tried but no. could you please walk me through it. :(

 

[I like Serena]

So which equations do you have now?
And what do you already know about the numbers in them?

 

[princesssuckz]

So which equations do you have now?
And what do you already know about the numbers in them?

just the ones you gave. i tried the first one. but i don't think it's right.
v²_f= 14m/s²+2(9.8m/s) (26 m)

 

[I like Serena]

just the ones you gave. i tried the first one. but i don't think it's right.
v²_f= 14m/s²+2(9.8m/s) (26 m)

Ah, well, let me explain:

$v_i$ is the initial speed. What is it?
$v_f$ is the final speed. What is it?
$a$ is the acceleration you have to calculate - it is not gravity!
$\Delta x$ is the change in position - you have that right.

 

[princesssuckz]

Ah, well, let me explain:

$v_i$ is the initial speed. What is it?
$v_f$ is the final speed. What is it?
$a$ is the acceleration you have to calculate - it is not gravity!
$\Delta x$ is the change in position - you have that right.

$v_i$= 14 m/s
i don't know the $v_f$.

 

[I like Serena]

$v_i$= 14 m/s
i don't know the $v_f$.

Initially the vehicle is in front of a red light.
At this time the vehicle has its initial speed.

After accelerating over a distance of 26 m, the vehicle achieves its final speed.

Try again?

 

[princesssuckz]

Initially the vehicle is in front of a red light.
At this time the vehicle has its initial speed.

After accelerating over a distance of 26 m, the vehicle achieves its final speed.

Try again?

hmm..so the $v_i$= 0
and the $v_f$= 14m/s

right?

 

[I like Serena]

Right!

 

[princesssuckz]

Right!

now what?

 

[I like Serena]

now what?

Fill in the numbers in the formula again.
You have all the numbers except "a".

Then solve the equation for "a" and you have your answer.Can you write down the formula again with the symbols replaced by the numbers as far as you know them?

 

[princesssuckz]

Fill in the numbers in the formula again.
You have all the numbers except "a".

Then solve the equation for "a" and you have your answer.


Can you write down the formula again with the symbols replaced by the numbers as far as you know them?

sorry if I'm being slow here. so should it be like this 14 m/s²= 0+2a(26 m) ?

 

[I like Serena]

Exactly!

Can you solve "a" from this equation?

 

[princesssuckz]

Exactly!

Can you solve "a" from this equation?

$${14 {m \over s^2}-26m \over 2}= {2 a \over 2}$$

$${14 {m \over s^2}-26m \over 2}= a$$

$${-12 \over 2} = a$$

$$-6 = a$$

it's wrong, right?

 

[I like Serena]

Yeah, sorry, it's wrong.

Let's go back to the equation:
(14 m/s)²= 2a(26 m)

From here you cannot subtract 26 m to bring it to the other side.
(You could already see that this wouldn't work, because the units (m/s)2 and m do not match, which they must for subtraction.)
You need to divide by 26 m to bring it to the other side.

Can you do that?