# Solve 1D Dynamics Problem: Can Car Stop Before Intersection?

• hydra03
In summary, a car of mass 1100kg traveling at a constant velocity of 60 km/hr, east, has a coefficient of friction of 0.45 between its tires and the road. The driver attempts to stop the car when the traffic light turns red, but the brakes fail. The question is whether the car, which is 35m before the intersection, will be able to come to a stop before entering the intersection. To determine this, the frictional force on the car must be calculated, which can then be used to find the acceleration. The bottom three kinematic equations are used to solve for this acceleration.
hydra03
1D Dynamics Problem!

## Homework Statement

A car of mass 1100kg is traveling at a constant velocity of 60 km/hr, east. The coefficient of friction between the tires and the road is 0.45.
The driver of the car sees the traffic light in front turning red and steps on the brake, only to find that the brakes are not working. If the car is 35m before the intersection when this happens, would it be able to come to a stop before entering the intersection?

F = ma
d = vt + 1/2at^2
vf = vi + at

## The Attempt at a Solution

I've fiddled around with the bottom three kinematic equations, but I don't seem to be getting anywhere..

hydra03 said:

## Homework Statement

A car of mass 1100kg is traveling at a constant velocity of 60 km/hr, east. The coefficient of friction between the tires and the road is 0.45.
The driver of the car sees the traffic light in front turning red and steps on the brake, only to find that the brakes are not working. If the car is 35m before the intersection when this happens, would it be able to come to a stop before entering the intersection?

F = ma
d = vt + 1/2at^2
vf = vi + at

## The Attempt at a Solution

I've fiddled around with the bottom three kinematic equations, but I don't seem to be getting anywhere..

It looks like you are supposed to assume the car is slowing down because of the 0.45 kinetic friction value. Start by trying to compute the acceleration a. To do that try to find the frictional force on the car first.

## What is 1D dynamics and how does it relate to a car stopping before an intersection?

1D dynamics refers to the study of motion in one dimension, such as the motion of a car on a straight road. In this problem, we are interested in whether the car can stop before reaching an intersection, which involves analyzing the car's speed, distance, and acceleration in one dimension.

## What factors affect a car's ability to stop before an intersection?

The main factors that affect a car's ability to stop before an intersection include its initial speed, the distance to the intersection, and its acceleration or deceleration. Other factors such as the condition of the brakes and the road surface can also play a role.

## How can we use equations of motion to solve this problem?

We can use the equations of motion, specifically the kinematic equations, to solve this problem. These equations relate the car's speed, distance, and acceleration, and can help us determine whether the car can stop before the intersection by plugging in the given values and solving for the unknown variable.

## What are some real-world applications of this problem?

This type of problem is relevant in many real-world situations, such as driving a car on a busy road, where a driver needs to assess whether they have enough time to stop before reaching an intersection. It can also be useful for engineers designing traffic signals and intersections to ensure safe stopping distances for vehicles.

## What are some limitations of solving this problem using 1D dynamics?

While 1D dynamics can provide a good estimate of a car's motion in a straight line, it does not take into account other factors that may affect a car's ability to stop, such as wind resistance or the car's weight distribution. Additionally, in real-world situations, a driver may have to make sudden changes in direction or encounter other obstacles, which cannot be accurately modeled using 1D dynamics.

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