Solve Kinematic Equations for Automobile Braking

[Physics 134]

Homework Statement

An automobile is traveling on a long, straight highway at a steady 75.0 mi/h (33.3 m/s) when the driver sees a wreck 150m ahead. At that instant, she applies the brakes (ignore reaction time). Between her and the wreck are two different surfaces. First there is 100m of ice, where the deceleration is only 1.00 m/s^2. From then on, it is dry concrete, where the deceleration is a more normal 7.00 m/s^2.

a. What was the car's speed just before leaving the icy portion of the road?
b. What is the total distance her car travels before it comes to a stop?
c. What is the total time it took the car to stop?

Homework Equations

x=xo+vot+1/2at^2
v^2=vo^2+2a(x-xo)
x=xo+1/2(v+vo)t

The Attempt at a Solution

If she is only going 33.3 m/s and the car is on 100 m of ice and the deceleration is 1.0m/s^2, wouldn't the car stop before it got to the concrete? This question is just not making sense to me.

 

[Angry Citizen]

The answer to your specific question (not the question asked) is found using equation #2 with V=0, v0=33, x0=0 and |a|=1. What is x with these values? Is its magnitude greater than 100?

 

[PeterO]

Homework Statement

An automobile is traveling on a long, straight highway at a steady 75.0 mi/h (33.3 m/s) when the driver sees a wreck 150m ahead. At that instant, she applies the brakes (ignore reaction time). Between her and the wreck are two different surfaces. First there is 100m of ice, where the deceleration is only 1.00 m/s^2. From then on, it is dry concrete, where the deceleration is a more normal 7.00 m/s^2.

a. What was the car's speed just before leaving the icy portion of the road?
b. What is the total distance her car travels before it comes to a stop?
c. What is the total time it took the car to stop?

Homework Equations

x=xo+vot+1/2at^2
v^2=vo^2+2a(x-xo)
x=xo+1/2(v+vo)t

The Attempt at a Solution

If she is only going 33.3 m/s and the car is on 100 m of ice and the deceleration is 1.0m/s^2, wouldn't the car stop before it got to the concrete? This question is just not making sense to me.

Think about this!

If the car had no deceleration on the ice, [there is not much of an deceleration] it would continue at a constant 33.3 m/s; taking only 3 seconds to cover the 100m.
since it is decelerating at 1.0 ms^-2 the speed would reduce to only 30.3 m/s in 3 seconds, so it would take a tiny bit more than 3 seconds to reach the end of the ice, traveling at slightly less than 30.3 m/s.

To get the exact figures involved you need to apply the kinematic equations.