Download Chris Khan 2007 Physics Chapter 2 Distance is the total length of a

Chris Khan 2007
Physics Chapter 2
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Distance is the total length of a route of travel, mainly using meter as the unit of length. Distance is always
positive. It is a scalar quantity because it has no direction associated with it, just magnitude.
Displacement (∆x), on the other hand, is the change in position and is not always positive. Displacement is not
always the same as distance. If you go somewhere and then come back to your original location, your distance
may be a few kilometers, but your displacement is 0. ∆x = xf – xi.
o If you go from your house to your friend’s house (2.1 mi), then to the grocery store (4.3 mi) and then
back to your friend’s house (4.3 mi), what is your distance and displacement? The distance would be
2.1 + 4.3 + 4.3 = 10.7 mi but the displacement would be only 2.1 mi since you went 4.3 miles then
returned.
Average speed = distance / elapsed time. The unit for average speed is meters per second.
o If you drive 4 mi at 30 mph and then 4 mi at 50 mph, is your average speed greater than, equal to, or
less than 40 mph? Since it takes 8 minutes to travel 4 mi at 30 mph and 4.8 minutes to travel 4 mi at
50 mph, it takes 12.8 minutes to travel 8 mi and therefore, the speed is 37.5 mph, which is less than 40
mph.
o How long will it take a bird going 4 m/s to go 7 m? Avg Speed = Distance / Time  Time = Distance
/ Avg Speed = 7 m / 4 m/s = 1.8 s.
Average velocity = displacement / elapsed time. The unit for average velocity is also meters per second. vavg
= ∆x / ∆t. Avg Velocity is more useful because it tells us the direction of an object since it may be negative.
Velocity is a vector quantity because it tells us magnitude and direction.
o An athlete sprints 50m in 8s, then stops and walks back in 40s. What is his sprint velocity? What is
his walking velocity? What is his average velocity? His sprint velocity is defined as ∆x/∆t = 50-0/8-0
= 50/8 = 6.25 m/s. His walking velocity is ∆x/∆t = 0-50/40s = -1.25 m/s. His average velocity is 0,
since ∆x is 0 since he returned to his original spot and displacement therefore is 0.
An x versus t graph makes it easy to visualize a particle’s motion because it helps us interpret average velocity.
The slope of a line connecting two points on an x versus t plot is equal to the average velocity during that time
interval.
When writing an x-vs-t equation, use the equation: x(t) = xo + vot + ½ at2.
Acceleration is the change of velocity with time. Acceleration can be due to change in speed and/or direction.
When velocity is constant, there is no change in acceleration. Average acceleration is defined as aavg = ∆v / ∆t
and is given in meters per second2. With acceleration, we use a v versus t graph. Deceleration is when velocity
decreases with time. For this, a is usually negative.
o If a car goes from 0 to 60 mph in 6.2 s, what is the average acceleration? Since 60 mph is 26.8 m/s, we
divide this by 6.2 s to get 4.3 m/s2.
o If a boat goes somewhere at 7.4 m/s and slows to a stop in 12.3 s, what is its average acceleration? aavg
= ∆v / ∆t = vf – vi / ∆t = 0 – 7.4 m/s / 12.3s = -7.4 m/s / 12.3s = -0.60 m/s2. *NOTE: ∆v is negative
because vf is 0 and vi is 7.4 since it comes to a stop after starting at 7.4m/s.
Constant acceleration is self-explanatory. v = vo + at is the constant acceleration equation of motion, which
shows velocity as a function of time, where vo is used for initial velocity and a is used for average acceleration.
With constant acceleration, a = aavg.
o If a ball is thrown up with an initial velocity of 8.2 m/s and the acceleration is -9.81 m/s2, what is its
velocity after 1 second? v = 8.2 m/s + (-9.81 m/s2)(1s) = -1.6 m/s.
vavg = ½(vo + v) is the constant acceleration equation of motion, which shows average velocity, where vo and v
are the two velocities.
x = xo + ½(vo + v)t is the constant acceleration equation of motion, which shows position as a function of time.
o The distance traveled by an object from t1 to t2 is equal to the area under the velocity curve between
those two times.
x = xo + vot + ½at2 is the constant acceleration equation of motion, which shows position as a function of time,
in terms of the acceleration.
o A racecar starts from rest and accelerates at 7.40 m/s2. How far has it traveled in 3 seconds? x = xo +
vot + ½(at2) = 0+0+½(at2)=½(at2)=½(7.40 m/s2)(1s)2=3.70 m.
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v2 = vo2 + 2a(x – xo) is the constant acceleration equation of motion, which shows velocity as a function of
position. It is also known as the time-independent equation.
o Plane A has acceleration a and takeoff speed vto. What is the minimum length of runway, ∆xA required
for this plane? ∆x = v2 – vo2 / 2a = ∆xA = vto2 / 2a.
If I want to stop my 2008 Mercedes-Benz SLR McLaren to show it off to my boys, who are 20 m away, and I
am driving at 11.4 m/s and decelerate at 3.8 m/s2, how close do I come in front of my boys? ∆x = v2 – vo2 / 2a
= 0 - vo2 / 2a = -(11.4m/s2)2 / 2 x -3.8 m/s2 = 17.1 m. 20 – 17.1m = 2.9 m in front of my boys. *NOTE: v is 0
because my car comes to a stop!
When talking about vertical motion, we talk about the y-direction rather than the x-direction. For this, we
change the x’s in the equations to y’s and change a to g since everything free falling (see below) is subject to the
force of gravity.
Free fall is an example of motion with constant acceleration, where an object falls freely under the influence of
gravity. Objects of different weight fall with the same constant acceleration—provided air resistance is small
enough to be ignored, like in a vacuum.
o Free fall is the motion of an object subject only to the influence of gravity.
o An object is in free fall as soon as it is released, whether it is dropped from rest, thrown downward, or
thrown upward.
 Terminal Velocity is reached when air resistance is equal to the force of gravity.
The symbol for acceleration produced by gravity is g, which is 9.81 m/s2. If we choose a coordinate system
with the positive direction upward, the acceleration in free fall is a = -g. If the positive direction is downward,
then free-fall acceleration is a = g.
o When vo increases, g has the same sign. When vo decreases, g has the opposite sign.
o If xo is zero and positive to be downward, then position as a function of time is x = ½gt2. Velocity as a
function of time is v = gt and velocity as a function of position is v = √2gx.
o A volcano shoots out a lava bomb. It takes the lava bomb 4.75s to go up and fall back down. What is
the initial speed? vo = ½ gt = ½(9.81 m/s2)(4.75s) = 23.3 m/s.
 What is its speed when it returns to the same level from which it was launched? v = vo – gt =
23.3 m/s – (9.81 m/s2)(4.75s) = -23.3 m/s.