# Velocity Problem #2: Solve for Distance Traveled

• lauriecherie
In summary, the conversation discusses the problem of a car braking on a dry road with good tires, with a constant deceleration of 4.06 m/s2. The first question asks for the time it takes for a car traveling at 23.6 m/s to stop, with the correct answer being 5.813 seconds. The second question asks for the distance traveled in this time, with multiple attempts but no correct answer given. Equations and attempts at a solution are provided, with the correct answer being 68.59 meters. The mistake was the use of the negative acceleration when calculating the distance traveled.
lauriecherie

## Homework Statement

On a dry road, a car with good tires may be able to brake with a constant deceleration of 4.06 m/s2.

(a) How long does such a car, initially traveling at 23.6 m/s, take to stop?
5.813 s This answer is correct.

(b) How far does it travel in this time?
I've tried 59.47 m and 137.1868 but Webassign says both are incorrect. I have no clue as to what I am doing wrong.

## Homework Equations

x(t)= initial position + final velocity * time

v(t)= (acceleration * time) + initial velocity

x(t)= .5 * (acceleration * (time^2)) + (initial velocity * time) + inital position

x= initial position * (average velocity * time)

average velocity= (final velocity - initial velocity) / (2)

(final velocity^2) - (initial velocity^2) = 2 * acceleration * change in position

## The Attempt at a Solution

I got 59.47 meters by pluging in part a, 5.813 seconds, into the position function.
Then I tried 137.19 meters after figuring that in 5.813 seconds at 23.6 m/s (I multiplied the two) it could travel 137.19.

Any ideas on what I am doing wrong?

x(t)= .5 * (acceleration * (time^2)) + (initial velocity * time)
= .5*(-4.06)*...
The acceleration is negative because it is slowing the car. Decelerating.

Delphi51 said:
x(t)= .5 * (acceleration * (time^2)) + (initial velocity * time)
= .5*(-4.06)*...
The acceleration is negative because it is slowing the car. Decelerating.

68.59 meters. Thanks! I really REALLY appreciate it. I'm seeing the little things I'm doing wrong now.

Super!

## 1. What is the formula for calculating distance traveled using velocity and time?

The formula for calculating distance traveled is distance = velocity x time.

## 2. Can you provide an example of how to solve for distance traveled using velocity and time?

For example, if a car is traveling at a velocity of 50 miles per hour for 2 hours, the distance traveled would be 100 miles (50 miles per hour x 2 hours = 100 miles).

## 3. How does changing the velocity or time affect the distance traveled?

Changing the velocity will directly affect the distance traveled, as the distance is directly proportional to the velocity. Increasing the velocity will result in a greater distance traveled, and decreasing the velocity will result in a shorter distance traveled. Similarly, changing the time will also affect the distance traveled, as the distance is directly proportional to the time. Increasing the time will result in a greater distance traveled, and decreasing the time will result in a shorter distance traveled.

## 4. What units should be used when solving for distance traveled?

The units for velocity should be consistent with the units for time. For example, if velocity is measured in miles per hour, time should be measured in hours. This will ensure that the resulting distance is measured in the appropriate units, such as miles.

## 5. Is it possible to use this formula to solve for distance traveled in non-linear motion?

Yes, this formula can be used to solve for distance traveled in both linear and non-linear motion. However, in non-linear motion, the velocity may vary over time, so the formula may need to be adjusted to account for this change in velocity.

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