# Speed of each vehicle after the collision?

• M Malone
In summary, Vehicle 1 was traveling east and Vehicle 2 was traveling north when the collision occurred. Vehicle 1 was traveling at a 35 mph and claims that he was approaching the intersection when he was hit from behind by Vehicle 2. Vehicle 2 states that he stopped at the stop sign and didn't see Vehicle 1 until the moment of impact. After the collision, both vehicles experienced wheel lock due to crash damage and skidded over asphalt and grass. The total work done by friction on the grass was greater for Vehicle 2.
M Malone

## Homework Statement

"Before the collision, vehicle #1 was traveling east and vehicle #2 was traveling north.
• The driver of vehicle #1 states he was traveling 35 mph as he approached the intersection. He continues to state that vehicle #2 ran the stop sign, pulling out in front of him and causing him to crash.
• The driver of vehicle #2 states that he stopped at the stop sign before pulling out, and did not see vehicle #1 until the moment of impact. (From the stop sign, vehicle #2 would have traveled 30 feet to the point of impact.
After the collision, both vehicles experience wheel lock due to crash damage and skidded over asphalt (μk = 0.72) followed by grass (μk = 0.35). Neither surface has any significant incline.
• Vehicle #1 skidded on 20 feet of asphalt and 30 feet of grass before coming to rest. The angle of departure for vehicle #1 was 45 degrees north of east.
The weight of vehicle #1 including occupants was 4300 lbs.
• Vehicle #2 skidded on 25 feet of asphalt and 35 feet of grass before coming to rest. The angle of departure for vehicle #2 was 35 degrees north of east.
The weight of vehicle #2 including occupants was 3150 lbs.
An acceleration test concluded that a vehicle such as vehicle #2 would have a maximum acceleration of 2.0 m/s^2 at the time of the accident.
...What was the speed of each vehicle after the collision?"

## Homework Equations

(I'm all over the place, but...)

KE = (1/2)(m)(v^2)
W = Fd(cosθ)
W = ΔKE
F(friction) = (μk)(F(normal)) = (μk)(mg)
KE1 + PE1 + W(external) = KE2 + PE2
J = FΔt = mΔv = Δp
p = mv

## The Attempt at a Solution

Originally, I used the fact that the work of friction is equal to the change in kinetic energy, so:

W(f) = ΔKE
(μk)(mg)(d)(cosθ) = (1/2)(m)(v^2)
√[2(μk)(g)(d)(cosθ)] = v

But this doesn't account for the change in surfaces, from asphalt to grass. Also, I'm not even sure if it properly accounts for the two-dimensions of the collision.

I'm aware that this is a 2D elastic collision problem, and understand how to split the x- and y-components of the velocity. However, I don't think I'm approaching this properly.

Any help would be greatly appreciated.
Thank you!

You're given the distances traveled on each surface type. Imagine that an accident surveyor laid a measuring tape out along the paths that each vehicle took and recorded the straight-line distances of each surface for both vehicles. So no need to invoke trajectory angles in this part of the question.

For each vehicle write an expression for the total work done by friction from impact to stopping on the grass. The total for a given vehicle will be the sum of the energy it lost on asphalt and on grass.

Last edited:

## 1. What factors determine the speed of each vehicle after a collision?

The speed of each vehicle after a collision is determined by the initial speed of the vehicles, the mass of the vehicles, and the angle and direction of impact. The type of collision, such as head-on or rear-end, can also affect the final speed of the vehicles.

## 2. Does the speed of each vehicle after a collision always equal the sum of their initial speeds?

No, the speed of each vehicle after a collision may not always equal the sum of their initial speeds. This is because some of the kinetic energy from the initial speeds may be lost during the collision due to factors such as friction and deformation of the vehicles.

## 3. How does the speed of each vehicle after a collision affect the severity of the impact?

The speed of each vehicle after a collision directly affects the severity of the impact. The higher the speed, the greater the impact force and potential for damage to the vehicles and occupants. This is why it is important for vehicles to slow down and follow safe driving practices to reduce the risk of high-speed collisions.

## 4. Can the speed of each vehicle after a collision be calculated?

Yes, the speed of each vehicle after a collision can be calculated using the principles of conservation of momentum and energy. This requires knowledge of the initial speeds and masses of the vehicles, as well as the angle and direction of impact. Advanced mathematical equations and computer simulations are often used to calculate the final speeds in a collision.

## 5. How can the speed of each vehicle after a collision be measured?

The speed of each vehicle after a collision can be measured using various methods, such as using speed sensors or analyzing the damage to the vehicles. In the case of a car accident, law enforcement agencies may use skid mark analysis and other forensic techniques to estimate the speeds of each vehicle involved in the collision.

• Introductory Physics Homework Help
Replies
9
Views
3K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
5K
• Introductory Physics Homework Help
Replies
1
Views
3K
• Introductory Physics Homework Help
Replies
18
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
9
Views
4K