Finding displacement through velocity and deceleration

In summary, 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). The displacement of the car is 18.75 meters.
  • #1
Grace204
14
1

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
 
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  • #2
Grace204 said:
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..
 
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  • #3
true, I didnt know how to add the subscript on top. But can you help me answer this?
 
  • #4
Your relevant equation is correct. Put the known values in that equation and solve for displacement.
s=(v2-u2)/2a
 
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  • #5
cnh1995 said:
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.
 
  • #6
Grace204 said:
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.
 
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  • #7
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?
 
  • #8
Grace204 said:
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?
 
  • #9
Grace204 said:
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.
 
  • #10
cnh1995 said:
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
 
  • #11
Grace204 said:
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?
 
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  • #12
Grace204 said:
m2/s2 divided by m/s2?
Yes. You can see s2 cancel each other and m2/m becomes m.
 
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  • #13
SteamKing said:
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)"
 
  • #14
Grace204 said:
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?
 
  • #15
Grace204 said:
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.
 
  • #16
Grace204 said:
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.
cnh1995 said:
s=(v2-u2)/2a
Now substitute a=-2 here, since the car is decelerating.
 
  • #17
Thank you so much for your help!
 
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Related to Finding displacement through velocity and deceleration

What is displacement?

Displacement is a measure of the change in position of an object. It is a vector quantity, meaning it has both magnitude and direction, and is typically measured in units of length, such as meters or feet.

How is displacement calculated?

Displacement can be calculated by multiplying an object's average velocity by the time it takes to travel that distance. This can be represented mathematically as Δx = v * t, where Δx is displacement, v is velocity, and t is time.

What is the relationship between velocity and displacement?

Velocity and displacement are closely related, as displacement is defined as the change in an object's position over time, and velocity is the rate of change of an object's displacement over time. In other words, velocity is the derivative of displacement with respect to time.

How does deceleration affect displacement?

Deceleration, also known as negative acceleration, is when an object's velocity decreases over time. This means that the object is traveling in the opposite direction of its initial velocity. Deceleration can cause a decrease in displacement, as the object is moving in the opposite direction of its initial displacement.

Can displacement be negative?

Yes, displacement can be negative. This means that the object has moved in the opposite direction from its starting point. For example, if an object starts at a position of 5 meters and ends at a position of 2 meters, its displacement would be -3 meters. This indicates that the object moved 3 meters in the negative direction from its starting point.

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