Name: ______________________________
Test on Chapter 1: Driving the Roads
(Part 3)
Period _____
CP Physics
Date: _________
E. Burns
For each of the problems below, be sure to show all work, including a labeled sketch, the equation
used, numbers plugged in, and answers with correct units. You may encounter unfamiliar
situations in which you need to apply concepts that you have learned. Just think it through and
show your work!
PROBLEM #1: A car is traveling down a road traveling at a constant velocity. A deer jumps into the middle of the road. The driver first reacts and then after reaction time hits the brakes and slows down to a
complete stop. The graph on the left represents the car’s motion while reacting. The graph on the right
represents the car’s motion while braking. Each shows the distance traveled for different velocities that
car could be going.
Car's reaction distance with constant reaction
time
Car's braking distance with an constant braking
acceleration
200
braking distance [m]
reaction distance [m]
40
30
20
10
0
150
100
50
0
0
20
40
60
0
average velocity [m/s]
20
40
60
initial velocity [m/s]
A] Look at the graph on the left. What is the relationship between reaction distance and average velocity?
How do you know?
B] Look at the graph on the right. What is the relationship between braking distance and average velocity? How do you know?
vf2= vo2 + 2ad
vf= vo + at
𝑣𝑎𝑣 = 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒⁄𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
𝑎𝑐 =
𝑣2
𝑅
d = vot + ½ at2
𝐹𝑐 = 𝑚𝑎𝑐
C] What is the total stopping distance for the driver who is going 30 m/s? Justify your answer! Show your
work!
Distance (m)
D] Draw a d-t graph and a v-t graph of the motion of the car from first sight of the deer to a complete stop.
The dashed vertical line represents the end of the driver’s reaction time and the beginning of braking.
Velocity (m/s)
Time (s)
Time (s)
vf2= vo2 + 2ad
vf= vo + at
𝑣𝑎𝑣 = 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒⁄𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
𝑎𝑐 =
𝑣2
𝑅
d = vot + ½ at2
𝐹𝑐 = 𝑚𝑎𝑐
Problem #2: A car approaches a 7-m wide intersection.
A] Design a safe 7-m wide intersection. Use reasonable estimates for the variables, and include your reasoning.
Variable Your Value Your Reasoning
vi
a
w
7-m
ty
tr
B] Use your values to calculate the GO Zone and the STOP Zone.
C] Sketch the intersection, showing the GO and STOP zones and either the Overlap or Dilemma Zone. Label all distances clearly.
vf2= vo2 + 2ad
vf= vo + at
𝑣𝑎𝑣 = 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒⁄𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
𝑎𝑐 =
𝑣2
𝑅
d = vot + ½ at2
𝐹𝑐 = 𝑚𝑎𝑐
Let’s change the yellow light model so that, instead of maintaining constant speed through the intersection, you accelerate through the GO Zone.
Therefore, instead of calculating the GO ZONE using a = 0 in the distance equation, you must use the car’s
positive acceleration as you hit the gas to make it through the yellow light.
D] Explain what effect this change has on each of the following, and explain why.
(i)
GO Zone
(ii)
STOP Zone
(iii)
Overall safety of your intersection.
E] Given your response to [D], why shouldn’t you accelerate every time you encounter a yellow light?
vf2= vo2 + 2ad
vf= vo + at
𝑣𝑎𝑣 = 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒⁄𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
𝑎𝑐 =
𝑣2
𝑅
d = vot + ½ at2
𝐹𝑐 = 𝑚𝑎𝑐
PROBLEM #3: A 615-kg racing car is moving at its maximum speed of 42 m/s around a circular
racetrack that has a 50 m radius.
a) What is the centripetal acceleration of the car?
b) What is the friction force required to keep the car on the road?
c) If 8800 Newtons of friction between the tires and the road are available, what will happen to the
car?
d) Name two things that can be done to the racetrack and/or the car in order to increase the
maximum speed at which the car can make the turn.
e) In the diagram to the right, the circle represents the track, and the box
represents the car. If the car was traveling clockwise when it hits
an icy patch on which there wasn’t enough friction, which way
would the car move? EXPLAIN. Also, draw an arrow to show
what you mean.
vf2= vo2 + 2ad
vf= vo + at
𝑣𝑎𝑣 = 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒⁄𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
𝑎𝑐 =
𝑣2
𝑅
d = vot + ½ at2
𝐹𝑐 = 𝑚𝑎𝑐