# Kinematics - How fast does the car stop?

• kenji1992
In summary, a car traveling at 32.0 m/s with an acceleration of -3.50 m/s2 will come to a stop in 9.14 seconds and travel a distance of 146.24 meters before stopping.
kenji1992
Kinematics -- How fast does the car stop?

## Homework Statement

A car is moving with a speed of 32.0 m/s. The driver sees an accident ahead and slams on the brakes, giving the car an acceleration of -3.50 m/s2. How far does the car travel after the driver put on the brakes before it comes to a stop?

vi=32 m/s

vf=

t=

a=-3.5 m/s2

delta-x=

## The Attempt at a Solution

How would this problem be solved? Does it require two steps?

Is Vf=0m/s and Vi= 32 m/s?

Because if that's the case, wouldn't I use the formula a=vf-vi/t

So:

-3.5 m/s2=(0 m/s - 32 m/s)/t

-3.5 m/s2 = (-32 m/s)/t

t= -32 m/s/-3.5 m/s2

t= 9.14 s

Then to find distance, use s=d/t, rearrange as d=s*t

d=32 m/s*9.14 s

d=292 m

Your "t" is correct, but your "d" is not. d=s*t is valid only when you have a constant s (rate), which is not the case here-- s is decreasing. Pick a relevant kinematic equation and you will be home free.

d=0.5(vi+vf)*t
d=0.5(0 m/s + 32 m/s)*9.14 s
d=146.24 m

Looks good. Watch your significant digits.

Therefore, the car travels 292 meters before coming to a stop. This solution assumes that the car stops at 0 m/s and that there are no other external forces acting on the car. It also assumes that the acceleration remains constant throughout the braking process. If these assumptions are not met, the solution may vary.

## 1. How is speed related to the car's stopping distance?

The speed of a car is directly related to its stopping distance. The faster the car is moving, the longer it will take to come to a complete stop. This is because the car has more momentum and requires more distance to slow down.

## 2. How does weight affect the car's stopping distance?

The weight of a car also plays a role in its stopping distance. A heavier car will have more momentum and require more distance to stop compared to a lighter car traveling at the same speed. This is why it's important to properly distribute weight in a car to optimize its braking capabilities.

## 3. What is the difference between stopping distance and braking distance?

Stopping distance refers to the total distance a car travels from the moment the brakes are applied until it comes to a complete stop. This includes the reaction time of the driver. Braking distance, on the other hand, only refers to the distance the car travels while the brakes are applied.

## 4. How does road condition impact the car's stopping distance?

The condition of the road surface can greatly affect a car's stopping distance. A wet, icy, or uneven road surface can reduce the amount of friction between the tires and the road, making it more difficult for the car to stop. This is why it's important to adjust driving habits in different weather conditions to account for changes in stopping distance.

## 5. Can the car's braking system affect its stopping distance?

Yes, the quality and condition of a car's braking system can greatly impact its stopping distance. Worn brake pads, low brake fluid, or other malfunctions can decrease the effectiveness of the brakes and increase the car's stopping distance. Regular maintenance and timely repairs are important for ensuring a car's brakes are functioning properly.

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