# Find the displacement in a word problem

• Natko
In summary, the original velocity of the car was 50 km/h and its final velocity was 5.0 m/s. Using the equation vf2 = v02 + 2aΔx, the distance traveled can be calculated by solving for Δx. After converting the units of acceleration from km/h/s to km/h/h, the correct answer is 15 m.
Natko

## Homework Statement

A car is slowing down at a rate of 20 km/h/s. How far does it travel if its original velocity is 50 km/h and its final velocity is 5.0 m/s?

vf2 = v02 + 2aΔx

## The Attempt at a Solution

vf2 = v02 + 2aΔx
Δx = (vf2 - v02) / 2a
= (182-502) / 2(-20)
= -2176 / -40
= 54.4 m

That's wrong, though. The answer should be 15 m.

Whoops, forgot to convert km/h/s to km/h/h. I got the answer now :)

Natko said:

## Homework Statement

A car is slowing down at a rate of 20 km/h/s. How far does it travel if its original velocity is 50 km/h and its final velocity is 5.0 m/s?

vf2 = v02 + 2aΔx

## The Attempt at a Solution

vf2 = v02 + 2aΔx
Δx = (vf2 - v02) / 2a
= (182-502) / 2(-20)
= -2176 / -40
= 54.4 m

That's wrong, though. The answer should be 15 m.

## 1. What is displacement in a word problem?

Displacement in a word problem refers to the distance between the initial and final positions of an object. It is a vector quantity and is typically measured in units such as meters or kilometers.

## 2. How is displacement different from distance?

Distance is the total length covered by an object, while displacement takes into account only the change in position. This means that displacement can be either positive, negative, or zero, while distance is always a positive value.

## 3. How is displacement calculated in a word problem?

To calculate displacement, you need to know the initial and final positions of the object. Simply subtract the initial position from the final position to find the displacement. If the displacement is in a straight line, you can use the formula D = xf - xi, where D is displacement, xf is final position, and xi is initial position.

## 4. Can displacement be negative?

Yes, displacement can be negative. This means that the object has moved in the opposite direction of the positive direction. For example, if an object moves from 5 meters to 2 meters, its displacement would be -3 meters.

## 5. How is displacement represented in a word problem?

Displacement is often represented by the symbol Δx (delta x) or simply by the letter D. It is also common to see the units of displacement written after the value, such as 5 meters or -3 kilometers.

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