Title: Theory / Unimportant / Experimental / Physics / Thinking physics

Question: Suppose you are going for a long bicycle ride. You ride one hour at five miles per hour. Then three hours at four miles per hour and then two hours at seven miles per hour. How many miles did you ride?
a) five
b) twelve
c) fourteen
d) thirty-one
e) thirty-six
Answer: The answer is: d. Remember speed multiplied by time is distance.
But what is the speed? It changes during the ride. So split the trip up
into segments. One hour at five mph gives five miles. Three hours at
four mph gives twelve miles and two hours at seven mph gives fourteen miles. Then add the segments. Five plus twelve plus fourteen sum to thirty-one. So that is the answer, that's it.
Yes, that is the answer, but that is not it. That is just some arithmetic.
Arithmetic is blind. Can you visualize what you are doing? To visualize, use geometry. Geometry has eyes.
Make a graph showing the history of the ride. For one hour it is at
five mph. Then it drops to four mph and stays there for three hours.
Then it jumps up to seven mph for two hours and finally it drops to zero which means the bike stops.
Now split the graph into three rectangles. Each rectangle represents one segment of the trip. The first rectangle is 5 mph high and 1 hour wide. What is the area of this rectangle? Multiply its height by its width-that is, multiply 5 mph by 1 hour-and you get 5 miles. The area of the rectangle is the distance covered during the first segment of the ride. Likewise the area of the second rectangle is 4 mph multiplied by 3 hours which is 12 miles. So the area of each rectangle is equal to the distance traveled on that segment of the ride.
That gives you a nice way to visualize distance traveled. Imagine a recording speedometer that gives you a graph of your speed plotted against time. The total area under the speed curve must tell how far you have traveled.

Question: A dragster starts from rest and accelerates to 60 mph in 10 seconds. How far does it travel during those 10 seconds?
a) 1/60 mile
b) 1/12 mile
c) 1/10 mile
d) 1/2 mile
e) 60 miles.

Question: At maximum acceleration from rest a dragster goes 1/10 of a mile in 10 seconds. What speed did it get up to in those ten seconds?
a) 6 mph, b) 52 mph, c) 60 mph, d) 62 mph, e) 72 mph.
Answer: Equation is maximum speed x time /2=distance,
max_speed = 2distance/time=2 x 1/10 / 1/360= 72

Answer: b)

Question: Two bicyclists travel at a uniform speed of 10 mph toward each other. At the moment when they are 20 miles apart, a bumble bee flies from the front wheel of one of the bikes at a uniform speed of 25 mph directly to the wheel of the other bike. It touches it and turns around in a negligibly short time and returns at the same speed to the first bike, whereupon it touches the wheel and instan- taneously turns around and repeats the back-and-forth trip
over and over again - successive trips becoming shorter and shorter until the bikes collide and squash the unfortunate bee between the front wheels. What was the total mileage of the bee in its many back-and-forth trips from the time the bikes were 20 miles apart until its hapless end?
(This can be very simple or very difficult, depending on
your approach.)
a) 20 miles
b) 25 miles
c) 50 miles
d) more
e) This problem cannot be solved with the information
given
Answer: b

Question: Dr. Pisani exercises his dog Sam on a 15-minute walk by throwing a stick that Sam chases and retrieves. To keep Sam running for the longest time as Dr. Pisani walks, which way should he throw the stick?
a) In front of him
b) In back of him
c) Sideways
d) In any direction as all are equivalent
Answer: d) because question asks for total time, and not time by throw, otherwise it would be b)

Question: The St. Charles Street streetcar is approaching Canal
Street at 144 inches per second. A person in the streetcar is
facing forward and walking forward in the car with a speed
of 36 inches per second relative to the seats and things in
the car. The person is also eating a Poor Boy which is
entering his mouth at 2 inches per second (he eats fast). An
ant on the Poor Boy is running to the end of the Poor Boy,
away from the person's mouth. The distance between the
ant and the end of the Poor Boy towards which it is run-
ning is closing at 1 inch per second. Now the question is:
How fast is the ant approaching Canal Street?
a) Zero in/s
b) 100 in/s
c) 170 in/s
d) 179 in/s
e) 180 in/s
Answer: d

Question: A stone is thrown straight upward and at the tippity top of its path its velocity is momentarily zero. What is its acceleration at this point?
a) Zero
b) 32 ft/s^2
c) Greater than zero, but less than 32 ft/s^2
Answer: b) accelleration is constant

Question: A motion picture film is made of a falling object which shows the object accelerating downwards. Now if the film is run backwards, it will show the object accelerating
a) upward
b) still downward
Answer: Surprise! The answer is: b. If the film is run backwards it will show the object moving up, but its acceleration will still be downward. Run the film backwards in your head. The ball is seen moving upwards initially fast, and then more slowly, just as if you threw it upward. Clearly the upward motion is not increasing so it could not be accelerating upwards. But the
speed is changing so it is accelerating, and a decrease of upward speed is a downward acceleration.
What this goes to show is something about rates of change. If time is reversed the rate of change of anything will reverse, that is the rate of change of anything will decrease if it was previously increasing. But if time is reversed the rate of change of the rate of anything will not reverse. Acceleration is the rate of change of velocity and velocity is the rate of change of position so acceleration is a rate of change of a rate of change
and that is why it did not reverse.
What about a rate of change of a rate of change of a rate of change - does it reverse when time reverses? Yes, it does reverse. What about the rate of change of the rate of change of the rate of change of the rate of change? It does not reverse when time reverses. Incidentally, there are symbols to represent these things which save a lot of words.
If \(X\) is the position of a thing then \(\dot X\) is the rate of change of position or speed of the thing, and \(\dot{\dot X}\) is the acceleration of the thing, and \(\dot{\dot {\dot X}}\) is the rate of change of the acceleration which is called the jerk, and \(\dot{\dot {\dot {\dot X}}}\) is the rate of change of the jerk which perhaps you can think up a good name for

Question: The battery output voltage, the bottle volume, the clock time, and the measure of weight all have something in common. It is that they are represented by
a) one number
b) more than one number.
Answer: a

Question: The pair of Levis, the bolt, the street intersection, and Ms. America all have something in common. It is that they are represented by
a) one number
b) a string of numbers.
Answer: b