Trying to find displacement using velocity and acceleration

In summary, the problem involves a train traveling at a velocity of 60.0 m/s and slowing down at a uniform rate of 1.25 m/s2. The goal is to find the distance the train will travel before its velocity is half of its original value. The equation used is v2 = vo2 + 2ad, where d represents the displacement or distance traveled. However, the attempt at solving the problem results in a negative value for d, which is not possible. The correct manipulation of the equation is d = (vo2 - v2)/2a, which yields a positive value for d. The confusion may have been caused by the incorrect placement of parentheses and the incorrect conversion of units.
  • #1
mrsconfused
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0

Homework Statement


A train traveling at a velocity of 60.0 m/s is slowed down at a uniform rate of 1.25 m/s2. How far will it travel before its velocity is 1/2 its original value?


Homework Equations


v2 = vo2 + 2ad


The Attempt at a Solution


I first need to isolate my variable, so 'd'. In which case, I believe the equation would then look like 'd=vo2 [itex]\div[/itex] v2+2a. Filling in this equation with the numbers then looks like: d=60m/s2[itex]\div[/itex]30m/s2+2(-1.25m/s2). But when I calculate it all out I'm left with d=-0.5m/s2. This does not make any sense though; it's not possible for the train to travel a negative amount of distance. And also, isn't displacement measured in units of length and not time? I can't figure out how to get rid of the seconds. Needless to say, I am very confused. Thanks in advance.
 
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  • #2
mrsconfused said:
I believe the equation would then look like 'd=vo2 [itex]\div[/itex] v2+2a.
I don't. Try that manipulation again. If you're still stuck, post your detailed working.
 

1. How do I calculate displacement using velocity and acceleration?

Displacement can be calculated by using the formula: displacement = initial velocity * time + (1/2) * acceleration * time^2. This formula assumes a constant acceleration rate.

2. What is the difference between velocity and acceleration?

Velocity is the rate of change of an object's position, while acceleration is the rate of change of an object's velocity. Velocity is a vector quantity, meaning it has both magnitude and direction, while acceleration is a scalar quantity, only having magnitude.

3. Can displacement be negative?

Yes, displacement can be negative. When an object moves in the opposite direction of its initial position, it has a negative displacement. For example, if an object starts at position 5 meters and moves to position 3 meters, its displacement would be -2 meters.

4. Is it possible to find displacement if only given acceleration?

No, displacement cannot be determined if only given acceleration. In order to calculate displacement, either initial velocity or final velocity must also be known.

5. How do I know if I should use the average or instantaneous velocity to calculate displacement?

If the object has a constant velocity, the average velocity can be used to calculate displacement. If the object has a changing velocity, the instantaneous velocity at a specific time should be used to calculate displacement.

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