How Do You Calculate Initial Speed and Time Elapsed in a Collision Scenario?

[darklich21]

Homework Statement

A motorist suddenly notices a stalled car and slams on the brakes, decelerating at the rate of 6.3 meters/second^2. Unfortunately this isn't good enough, and a collision ensues. From the damage sustained, police estimate that the car was moving at 13 kilometers/hour at the time of the collision. They also measured skid marks 33 meters long. How was was the motorist going when the brakes were first applied? How much time elapsed from the inital brraking to the collision?

Homework Equations

Vf^2=Vi^2 + 2ad
Vf=Vi + at

The Attempt at a Solution

Alright so to answer the first question, I used the first equation above.
0=Vi^2 + 2(-6.3m/s^2)(33m)
Vi= 20.4 m/s

To answer the 2nd question, I just used Vf= Vi + at
0=20.4m/s + 2(-6.3m/s^2)(t)
t=1.62 seconds

This all seems right, but the fact that the car is moving at 13 km/hour is bothering me. Is it useless data? or is it meant to be used in such a way? Please help.

 

[darklich21]

Ok so I did the first part right, but my 2nd part was wrong. I think the car is factored in somehow, can anyone help?

 

[rl.bhat]

The motorist is decelerating. At the time of collision his velocity is 13 km/h. It cannot be the velocity of stalled car. You cannot assume that the motorist comes to rest immediately after collision.

 

[darklich21]

So if I'm understanding this right, you're saying my Vf in the 2nd equation should be the same as the speed of the car when he crashed?

 

[rl.bhat]

So if I'm understanding this right, you're saying my Vf in the 2nd equation should be the same as the speed of the car when he crashed?

According to the conservation of the momentum, it depends on the masses of the cars.

 

[darklich21]

Well neither mass is given, but if they want to know how much time elapsed from the initial braking to the collision, I'm thinking in the process of him braking, that car is still moving. Wouldn't you think I need to factor that in somehow? Because if the car is still moving while he's braking before he collides in it, the time would be extended, no?

 

[rl.bhat]

Time required is the interval between the instant of applying brakes to the instant of the collision.

 

[darklich21]

So how would I go about solving how much time elapsed from the inital brraking to the collision? What equation would I use?

 

[rl.bhat]

Use x =[ ( vi + vf )/2]*t

 

[darklich21]

well ok, x would be 33m, Vi would be 20.4m/s, I am solving for t, but what's my Vf? would it be 0 since it crashed? That's what I'm not getting here.

 

[rl.bhat]

well ok, x would be 33m, Vi would be 20.4m/s, I am solving for t, but what's my Vf? would it be 0 since it crashed? That's what I'm not getting here.

I am nor sure about it. At the instant of collision, its velocity cannot be zero. In that case there will not be much dent in the car.