Module 2
Presentation Question & Answers
Question 1:
Question 1:
A car traveling at 35 m/sec (about 78 mph) passes a police car which is moving at
23 m/sec (about 51 mph). The policeman does not have a radar gun, so he
immediately starts to speed up in order to match the speeder's velocity. That
way, he will be able to measure how fast the speeder is moving. If the police car
can accelerate at a rate of 2.5 m/sec2, how long will it take for the policeman to
match the speeder's velocity?
Correct Answer:
This problem gives us the final velocity that the police car needs (35 m/sec). It
also tells us the acceleration (2.5 m/sec2) and the initial velocity (23 m/sec).
Since the policeman is speeding up, the acceleration and velocity have the same
sign. Thus, to make things easy, we will define the direction that the cars are
moving as positive motion. The problem asks us to solve for time. Equation (2.6)
relates all of those things, so that's what we'll use:
Vfinal or v = 35 m/sec
Vinitial or Vo = 23 m/sec
a = 2.5 m/sec2
t=?
v = vo + at
Now we can use algebra to rearrange the equation and solve for time:
t=
v - vo
a
We've determined, therefore, that the policeman needs 4.8 sec to match the
velocity of the speeder.
Question2:
A car has a maximum acceleration of 11,500 miles/hour2. If it starts from rest
and accelerates as quickly as possible for 500 yards, what will its velocity be?
(There are 1760 in a mile).
Correct Answer:
vo = 0
a = 11,500 miles/hour2
x = 500 yards
v=?
500 yards
1
1 mile
x
=
.284 miles
1760 yards
11,500
6,532
6,532
The car can go from 0 to 80.8 mph in just 500 yards.
Question 3:
A race car starts at rest and travels 1,321 ft (a quarter of a mile) in 11 seconds.
What was the car's acceleration?
Correct Answer:
vo = 0
t = 11 sec
x = 1,321 ft
a=?
The race car, then, had an acceleration of 22 ft/sec2.
Question 4:
If a car can accelerate from rest to a velocity of 60.0 miles per hour in 10.0
seconds, what is its acceleration?
Correct Answer:
vo = 0
v = 60 miles/hour
t = 10 sec
a=?
This car, then, has an acceleration of 21,600 miles/hour2
Question 5:
In order to take off, a certain plane needs to start from rest and achieve a velocity
of 150 miles/hour before it reaches the end of the runway. If the plane's
acceleration is 20,000 miles/hr2, what is the minimum length needed for a
runway?
Correct Answer:
vo = 0
v = 150 miles/hour
a = 20,000 miles/hour2
?
v2 - vo2
2a
150
20,000
22,500
Question 5:
Question 40,000
5:
Question 6:
A biker can maintain a constant acceleration of 0.030 m/sec2. If the biker starts
from rest, how far can she travel if she keeps that acceleration up for 5.0
minutes?
Correct Answer:
vo = 0
a = 0.030 m/sec2
t = 5.0 min
?
To make the units agree, I will convert minutes to seconds:
300
Now that we have our data in consistent units, we can use the equation:
300
300
90,000
1,350
The biker, then, can travel 1,350 meters or (1,400 meters in significant digits) in
5.0 minutes with that acceleration.
Question 7:
How long will it take a rock to hit the ground if it is dropped from the Leaning
Tower of Pisa (height = 54.6 m)?
Correct Answer:
We know that the object is in free fall, because it is falling near the surface of the
earth, and we always neglect air resistance. Thus, we know its acceleration to be
-9.8 m/sec2. A negative acceleration means we have defined downwards motion
as negative. We also know the displacement is -54.6 meters. The displacement is
also negative, because the object will travel 54.6 meters down. In addition, we
know that if it is dropped, the initial velocity is zero. So we know displacement,
initial velocity, and acceleration, and we want to determine the time. Equation
(2.19) relates all of these quantities and, since all of our units are consistent, we
can simply plug in our numbers and solve for time:
x = -54.6 m
v0 = 0
a = -9.8 m/sec2
t=?
So it takes 3.3 seconds for an object to fall from the Leaning Tower of Pisa.