RNT1 Lecture Notes - Lecture 2: Equations For A Falling Body, Net Force, Scientific Method

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26 Sep 2019
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Example: A Trip Home - Suppose you are visiting a friend. It is time to leave and you remember
that you have to pick up a quart of milk on the way home. Your route is shown in the figure
below. We want to calculate your average speed on the way home and your average velocity on
the way home.
First, let’s calculate your average speed. We need to know the total distance traveled, which is
just the sum of the distance from your friend’s house to the store and the distance from the store
to your home:
W
e
al
so
need to find the time for the trip, which is the sum of the time to travel from your friend’s house
to the store, the time to buy the milk, and the time to travel from the store to your home:
This is a little harder because we don’t know times for the traveling parts of the trip. However,
we know that the time to travel a certain distance at a certain speed is just the ratio of the
distance to the speed, so we have
So we get for your average speed:
The average velocity uses the same time, since the time in both cases is just the time for the
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whole trip. However, as we know, the numerator is the change in coordinate. Your final
coordinate is the coordinate of your home and your initial coordinate is the coordinate of your
friend’s house. So, the average velocity is
We see that they are substantially different and have opposite signs!
Instantaneous Velocity and Speed
The instantaneous speed of a particle is the speed that it has at a single instant of time. The
speedometer in your car measures your instantaneous speed. At the instant the needle on your
speedometer crosses the 35 mph line, you are traveling 35 mph.
Instantaneous velocity is the velocity at an instant of time.
Note that, in one dimension, instantaneous speed and velocity always have the same numerical
size. This is due to the fact that, at an instant of time, it is not possible for a particle to travel
past a point and then back.
The difference is direction. Speed is always positive, but velocity is positive for motion to the
right and negative for motion to the left (given a standard number line as a coordinate system).
In one dimension, instantaneous speed is the absolute value of the instantaneous velocity.
Speed is how fast. Velocity is how fast and in what direction.
What happens if the velocity changes? Acceleration!
Acceleration
Acceleration is the rate at which velocity changes.
Acceleration can involve a change in speed, a change in direction, or both.
Note that a decreasing velocity is also an acceleration.
A deceleration is an acceleration that is opposite the velocity.
Note that the speed can be constant and a body can still accelerate because the direction of its
motion changes — moving round in a circle with constant speed.
Since acceleration is defined as the rate at which velocity changes, the average acceleration is
given by the change in velocity divided by the time taken for the change to take place. In
symbols,
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