# Stopping Distance and kinetic friction

• David Donald
In summary, the question asks for the final stopping distance of a 1000kg car, traveling at 115.2 km/h on a highway with a disabled ABS system. The car must rely solely on the friction of its tires to stop. A deer jumps 50 meters in front of the car and the frictional force applied by slamming on the brakes is 4000N. The attempt at a solution involves calculating the acceleration of the car using a sum of forces in the x direction, resulting in an incorrect time and distance. Further considerations should be made regarding the acceleration of the car and its starting velocity.
David Donald

## Homework Statement

While traveling on the highway with your 1000kg car, at 115.2 km/h, where you’re ABS (automatic

braking system) is disabled. This means braking is relying solely on the friction of your tires with the road when they stop spinning. A dear jumps into the road 50 meters in front of you. If the frictional force created by you slamming on your brakes is 4000N. What will your final stopping distance be? Will you

hit the dear? Assume no air resistance.

Kinematics?

## The Attempt at a Solution

Sum of Forces in The X direction
(Force O' Car) - (Force O' Friction) = -ma

I solved for acceleration and got -5.8 m/s^2
plugging these into the kinematics equation I got a time... 5.52 seconds
plugging that into the Xf = Xo + Vox t + 1/2 a t^2 I got a distance which is wrong

what gives? what am i doing wrong?

Maybe look at the momentum of the car. Units will be N sec. What would be a reasonable way to find seconds to stop under friction force in N?
I get something greater than 6 seconds.

David Donald said:

## Homework Statement

While traveling on the highway with your 1000kg car, at 115.2 km/h, where you’re ABS (automatic

braking system) is disabled. This means braking is relying solely on the friction of your tires with the road when they stop spinning. A dear jumps into the road 50 meters in front of you. If the frictional force created by you slamming on your brakes is 4000N. What will your final stopping distance be? Will you

hit the dear? Assume no air resistance.

Kinematics?

## The Attempt at a Solution

Sum of Forces in The X direction
(Force O' Car) - (Force O' Friction) = -ma

I solved for acceleration and got -5.8 m/s^2
plugging these into the kinematics equation I got a time... 5.52 seconds
plugging that into the Xf = Xo + Vox t + 1/2 a t^2 I got a distance which is wrong

what gives? what am i doing wrong?
We have no idea; you didn't provide your complete calculations.

BTW, "you're" = "you are" and shouldn't be used to mean "your".

By the way...what is the acceleration caused by 4000N on a 1000kg car? If the car is starting at a constant velocity, that means acceleration of the car is zero...so what is the acceleration in the system? It is not -5.8 m/sec^2.

## What is stopping distance?

Stopping distance is the distance that a moving object travels before it comes to a complete stop. It is influenced by factors such as the speed of the object, the surface it is moving on, and the force of friction.

## What is kinetic friction?

Kinetic friction is the force that occurs when two surfaces are in contact and in relative motion to each other. It is caused by microscopic bumps and ridges on the surfaces that interact with each other, slowing down the motion of the object.

## How is stopping distance affected by kinetic friction?

Stopping distance is directly affected by kinetic friction. The greater the force of kinetic friction, the longer the stopping distance will be. This is because the force of friction acts in the opposite direction of the object's motion, causing it to slow down and travel a greater distance before coming to a stop.

## How do you calculate stopping distance?

Stopping distance can be calculated using the formula: d = (v2)/2μg, where d is stopping distance, v is initial velocity, μ is the coefficient of kinetic friction, and g is the acceleration due to gravity (9.8 m/s2).

## What factors can affect the coefficient of kinetic friction?

The coefficient of kinetic friction can be affected by several factors, including the roughness of the surface, the type of material, and the amount of force pressing the two surfaces together. It can also be affected by the presence of lubricants or other substances between the two surfaces.

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