Finding displacement through velocity and deceleration

[Grace204]

Homework Statement

a car with an initial velocity of 10.0 m/s (W) decelerates at -2.00 m/s (s to the power of 2) (W) reaching a final velocity of 5.00 m/s (W). What is the displacement of the car?

Homework Equations

Δdisplacement = (final velocity to the power of 2 - initial velocity to the power of 2)/ 2 times acceleration

The Attempt at a Solution

I didn't really get far because I didn't know how to deal with the units and the minus/plus signs

 

[cnh1995]

decelerates at -2.00 m/s

I believe it should rather be 'accelerates at -2m/s²'. Negative acceleration is deceleration and negative deceleration is acceleration..

 

[Grace204]

true, I didnt know how to add the subscript on top. But can you help me answer this?

 

[cnh1995]

Your relevant equation is correct. Put the known values in that equation and solve for displacement.
s=(v²-u²)/2a

 

[Grace204]

Your relevant equation is correct. Put the known values in that equation and solve for displacement.
s=(v²-u²)/2a

I don't know how to. The anwer I am getting is -18.75, and i don't think that's right.

 

[cnh1995]

I don't know how to. The anwer I am getting is -18.75, and i don't think that's right.

It is negative because you used a=2m/s²
Since the car is decelerating, you should use a=-2m/s²..
Then you'll get it as 18.75m.

 

[Grace204]

This is what i did-
(5.00 m/s [W])² - (10.0 m/s [W])² / 2 * -(-2.00 m/s²
(-5.00 m/s)² - (-10.0 m/s)² / 4.00 m/s²
After this, what happens to the units? How do the s² cancel each other out?

 

[Grace204]

This is what i did-
(5.00 m/s [W])² - (10.0 m/s [W])² / 2 * -(-2.00 m/s²
(-5.00 m/s)² - (-10.0 m/s)² / 4.00 m/s²
After this, what happens to the units? How do the s² cancel each other out?

Do the units become m²/s² divided by m/s²?

 

[cnh1995]

This is what i did-
(5.00 m/s [W])² - (10.0 m/s [W])² / 2 * -(-2.00 m/s²
(-5.00 m/s)² - (-10.0 m/s)² / 4.00 m/s²
After this, what happens to the units? How do the s² cancel each other out?

Yes. And only the unit of displacement remains which is meter..Every equation has to be dimensionally correct.

 

[Grace204]

Yes. And only the unit of displacement remains which is meter..Every equation has to be dimensionally correct.

So s² divided by s² cancels each other out and does not equal s⁴? Because acceleration is m/s divided by s

 

[SteamKing]

This is what i did-
(5.00 m/s [W])² - (10.0 m/s [W])² / 2 * -(-2.00 m/s²
(-5.00 m/s)² - (-10.0 m/s)² / 4.00 m/s²
After this, what happens to the units? How do the s² cancel each other out?

Why did you put double negative signs on the acceleration in the denominator?

You should be able to work out the resulting units using standard algebra.

If you square velocity in m/s, what do you get?

If you divide these units for velocity squared by the units for acceleration, what's left?

 

[cnh1995]

m2/s2 divided by m/s2?

Yes. You can see s² cancel each other and m²/m becomes m.

 

[Grace204]

Why did you put double negative signs on the acceleration in the denominator?

You should be able to work out the resulting units using standard algebra.

If you square velocity in m/s, what do you get?

If you divide these units for velocity squared by the units for acceleration, what's left?

I put double negatives on the denominator because the question says is "decelerates at -2.00 m/s² [W] or -(-2.00 m/s²)"

 

[Grace204]

I put double negatives on the denominator because the question says is "decelerates at -2.00 m/s² [W] or -(-2.00 m/s²)"

Is this wrong? If so, how would I write this out?

 

[SteamKing]

Is this wrong? If so, how would I write this out?

The question is poorly worded. One negative sign should suffice, since 'decelerate' means to reduce speed or velocity.

 

[cnh1995]

Is this wrong? If so, how would I write this out?

The initial and final velocities are 10m/s and 5m/s respectively. This clearly tells you that the car is 'decelerating'. So, you should write either 'a car is decelerating at 2m/s²' or ' a car is accelerating at -2m/s²'. That's what I meant in #2.
You should write the equation in the following form.

s=(v2-u2)/2a

Now substitute a=-2 here, since the car is decelerating.

 

[Grace204]

Thank you so much for your help!