# Determine distance with constant acceleration

• brunettegurl
In summary, a particle moving at 5m/s changes its direction in 1s and moves at 5m/s in the opposite direction. With a constant acceleration, the total distance traveled is 10m, with 5m in one direction and 5m in the other. The correct equation to use is x=(-5)(0.5)+ (0.50)(10)(0.5)^2, giving a displacement of 5m and doubling this value gives the total distance of 10m.
brunettegurl

## Homework Statement

A particle moving at 5m/s reverses its direction in 1 s to move at 5m/s in the opposite direction. If its acceleration is constant, what distance does it travel?

## Homework Equations

x=vot+0.5at^2; a=(vf-vi)/t

## The Attempt at a Solution

total time is 1s therefore acceleration is 10m/s^2 and then I'm stuck because when I input the value into the equation I'm not getting the answer of 2.5m which is the correct answer.

hi brunettegurl!

i think it means that it goes 1.25m in 0.5s, and then 1.25m back again, = 2.5m

try again

That's slightly tricky because in the equation you gave x is not the distance traveled but merely a coordinate describing the location. To highlight the difference: if I go for a stroll and come back home then my location will be the same as before, but I obviously traveled some distance. In your case, if you properly plugged in all values (taking into account the relative signs, because the acceleration is in opposite direction than the starting velocity) you should have ended up with x=0, which is completely correct but not the sought-for variable.
The solution to your problem is to realize that the distance traveled consists of a part that the particle moved to positive x-direction and a part where it traveled into negative x-directions. Treat these two parts separately and you get the correct result.

btw.: In the future, please also give the incorrect result you got, because that can greatly help understanding what went wrong.

Hi

I'm still a little confused my book states that to find distance we use half the total time in the equation w/accleration and then solve for x by doubling the answer for total distance by doing this ::

a=(5-(-5))/0.5= 20m/s^2

and when plugged into the equation x=(-5)(1)+ (0.50)(20)(1)^2
x(displacemnt)=5m and doubling this answer gives 10m

tiny-tim how did you get 1.25 as the distance traveled in 0.5s??

Thanks

hi brunettegurl!

no, it's not 20 m/s2, it's still 10, isn't it?

Im sorry how is it still 10 when you divide by time which is 0.5 now according to the explanation (1/2 the time) making the 10 now a 20 as acceleration

brunettegurl said:
[A particle moving at 5m/s reverses its direction in 1 s to move at 5m/s in the opposite direction. If its acceleration is constant, what distance does it travel?

it goes from +5 to -5 in 1 s (or from +5 to 0 in 0.5 s) …

that's 10 !

ohhh so for acceleration the vf would be 0 and vi would be +5 giving the acceleration of 10 .. correct?

so then when we sub in the values in x=(5)(1)+ (0.50)(10)(1)^2
i still get an x(displacemnt) value of =10m and doubling this answer gives 20m

do i continue to use 0.5 as my time value and then since it is reversing in the same scalar value of 5 just dbl the new x-value??

brunettegurl said:
so then when we sub in the values in x=(5)(1)+ (0.50)(10)(1)^2
i still get an x(displacemnt) value of =10m and doubling this answer gives 20m

(try using the X2 icon just above the Reply box )

that 1 should be 0.5, and that + should be -

Ok Thanks I understand now ... I think what confused me when I was reading the explanation in my book was the implication that 2 different time values were to be used... Thank you :)

## 1. How is distance determined with constant acceleration?

Distance is determined by using the formula d = 1/2at^2, where d is the distance, a is the acceleration, and t is the time.

## 2. What is constant acceleration?

Constant acceleration is when an object's velocity changes by the same amount over equal intervals of time.

## 3. What is the importance of determining distance with constant acceleration?

Determining distance with constant acceleration is important in understanding the motion of objects and predicting their future positions. It is also used in various real-world applications such as designing roller coasters and calculating the trajectory of projectiles.

## 4. How does the direction of acceleration affect the distance traveled?

The direction of acceleration does not affect the distance traveled. The distance traveled is only dependent on the magnitude of acceleration and the time elapsed.

## 5. Can distance be determined with constant acceleration if the initial velocity is not zero?

Yes, distance can still be determined with constant acceleration even if the initial velocity is not zero. The formula d = 1/2at^2 can be modified to include the initial velocity as d = Vot + 1/2at^2, where Vo is the initial velocity.

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