# Distance covered by car while decelerating

• 11NEPHILEM11
In summary, the car starts with an initial velocity of 15m/s and decelerates uniformly to a final velocity of 0m/s in 20 seconds. Using the equation X=Vit+(1/2)at^2, we can find the distance covered while decelerating. Alternatively, we can also find the area under the velocity-time graph, which will be a triangle, to determine the distance covered. With initial and final velocities, as well as time given, the only unknown is the acceleration, which can be found by rearranging any of the three kinematic equations.
11NEPHILEM11

## Homework Statement

A car level on ground, starting from 15m/s, decelerates uniformly to rest in 20 seconds. What distance does the car cover while decelerating?

## Homework Equations

Vf = Vi+at
Vf^2=Vi^2+2aX
X=Vit+(1/2)at^2

X = Distance
Vf = Final velocity
Vi = Initial velocity
a = acceleration
t = time

## The Attempt at a Solution

I started with the X=Vit+(1/2)at^2 formula and attempted to plug in the numbers but I have no idea how to find acceleration. I mean, I know acceleration is Δv over Δt but how am I supposed to find the final velocity when I need the acceleration to plug in the formula? I'll admit I zoned out a little in my last class because I was tired from work the day before.

Since you only have three kinematic equations, you will need to use two of them.
Note - you have initial and final velocities, and the time ... what is the acceleration?

The other approach is to sketch a velocity-time graph.
The distance covered is the area under the graph ... which will be a triangle.
You know how to find the area of a triangle right?

Are you sure you haven't listed an equation above, where you know 1. the initial velocity, 2. the final velocity, 3. the duration for the change in velocities, and 4. which leaves only acceleration (or deceleration) to be determined?

You have to understand what your relevant equations mean.

If I am understanding correctly, I already have my initial and final velocity? If my initial velocity is 15m/s then what is my final velocity? 0?

11NEPHILEM11 said:
If I am understanding correctly, I already have my initial and final velocity? If my initial velocity is 15m/s then what is my final velocity? 0?
Easy to check - the question says that the car "decelerates to rest" ... so what does that tell you about the final velocity?

## 1. What factors affect the distance covered by a car while decelerating?

The distance covered by a car while decelerating is influenced by several factors, such as the initial speed of the car, the rate of deceleration, the weight of the car, and the friction between the tires and the road surface.

## 2. How can I calculate the distance covered by a car while decelerating?

To calculate the distance covered by a car while decelerating, you can use the equation: distance = (initial speed)^2 / (2 x deceleration). This equation is based on the principle of conservation of energy and assumes that the deceleration is constant.

## 3. Does the type of road surface affect the distance covered by a car while decelerating?

Yes, the type of road surface can significantly impact the distance covered by a car while decelerating. A rough or slippery road surface can increase the friction between the tires and the road, resulting in a shorter stopping distance. On the other hand, a smooth and dry road can reduce friction and increase the stopping distance.

## 4. How does the weight of the car affect the distance covered while decelerating?

The weight of the car plays a crucial role in determining the distance covered while decelerating. A heavier car will have more momentum, making it harder to slow down, resulting in a longer stopping distance. On the other hand, a lighter car will have less momentum and can stop in a shorter distance.

## 5. Can the distance covered by a car while decelerating be affected by external factors?

Yes, external factors such as wind, incline, and curves in the road can influence the distance covered by a car while decelerating. For example, a strong headwind can increase the drag on the car, making it harder to slow down and resulting in a longer stopping distance. Similarly, an incline can increase the potential energy of the car, requiring more force to slow down and increasing the stopping distance.

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