Thursday 5/21
PHYS 2010
Nathalie Hoffmann
University of Utah
Position/Velocity vs. Time graphs
Position/Velocity vs. Time graphs
Free Fall
• Motion in the vertical (y) direction
• Constant acceleration due to gravity
• 𝑎 = −𝑔 = −9.8
𝑚
𝑠2
(near the surface of the Earth)
• Upward motion: speed decreasing
• Downward motion: speed is increasing
• Transition point: instantaneously at rest
Free Fall
Linear motion equations & when to use them
• No acceleration (a = 0)
• Constant velocity
• 𝑥𝑓 = 𝑥0 + 𝑣𝑥 𝑡
• 𝑦𝑓 = 𝑦0 + 𝑣𝑦 𝑡
• ∆𝑥 = 𝑣𝑥 𝑡
• ∆𝑦 = 𝑣𝑦 𝑡
Linear motion equations & when to use them
• Constant, non-zero acceleration
• Kinematics equations
1
• 𝑥𝑓 = 𝑥0 + 𝑣𝑥,0 𝑡 + 𝑎𝑥 𝑡 2 same as
2
1
• 𝑦𝑓 = 𝑦0 + 𝑣𝑦,0 𝑡 + 𝑎𝑦 𝑡 2 same as
2
1
∆𝑥 = 𝑣𝑥,0 𝑡 + 𝑎𝑥 𝑡 2
2 1
∆𝑦 = 𝑣𝑦,0 𝑡 + 𝑎𝑦 𝑡 2
2
• 𝑣𝑥,𝑓 = 𝑣𝑥,0 + 𝑎𝑥 𝑡
• 𝑣𝑦,𝑓 = 𝑣𝑦,0 + 𝑎𝑦 𝑡 = 𝑣𝑦,0 − 𝑔𝑡
2
2
2
• 𝑣𝑥,𝑓
= 𝑣𝑥,0
− 2𝑎𝑥 ∆𝑥 = 𝑣𝑥,0
− 2𝑎𝑥 (𝑥𝑓 − 𝑥0 )
2
2
2
• 𝑣𝑦,𝑓
= 𝑣𝑦,0
− 2𝑎𝑦 ∆𝑦 = 𝑣𝑦,0
− 2𝑎𝑦 (𝑦𝑓 − 𝑦0 )
• Note: when 𝑡𝑖 ≠ 0, then 𝑡 above should be ∆𝑡 = 𝑡𝑓 − 𝑡𝑖
Table 2-4
Test Taking Tips
• UNITS! Do not forget about them!
• Show ALL work! That means:
• Show the original formula (without numbers!)
• Show all your intermediate steps, e.g. calculations, rearranging of equations,…
• Write down any assumptions you make, anything that is not EXPLICITLY stated in/by
the problem statement
• Correct WORK is MORE IMPORTANT than correct answers
• Did I mention units? No? Well, they’re important.
Test Taking Tips
• Pretty PLEASE box or clearly mark/identify your final answer!
• Don’t give us more than one answer. More than one answer is
typically worse than no answer.
• Remember: READ the problem TWICE OR MORE TIMES.
• Write LEGIBLY.
Conceptual Question
• Suppose I drop a feather and bowling ball, from the same height,
inside a vacuum chamber on the surface of the Earth; what happens?
• Now, I drop a feather and a bowling ball, from the same height, on
the surface of the Moon; what happens?
• Compare & contrast the two scenarios
Time for practice problems
• Kevin completes his morning workout at the pool. He swims 4000
m (80 laps in the 50-m-long pool) in 1.00 h. (a) What is the average
velocity of Kevin during his workout? (b) What is his average
speed? (c) With a burst of speed, Kevin swims one 25.0-m stretch in
9.27 s. What is Kevin’s average speed over those 25 m?
• A runner starts from rest and achieves a maximum speed of 8.97 m/s.
If her acceleration is 9.77 m /s2, how far does she travel in the time it
takes her to reach that speed?
More Problems
• A fox locates its prey, usually a mouse, under the snow by slight sounds the
rodents make. The fox then leaps straight into the air and burrows its nose
into the snow to catch its next meal. If a fox jumps to a height of 85.0
cm, calculate (a) the speed at which the fox leaves the snow and (b) how
long the fox is in the air. Ignore the effects of air resistance.
• Wes stands on the roof of a building, leans over the edge, and drops a
rock. Lindsay waits 1.25 s after Wes releases his rock and throws her own
rock straight down at 28.0 m/s. Both rocks hit the ground
simultaneously.Calculate the common height from which the rocks were
released. Ignore the effects of air resistance.
More Problems
• Two trains, traveling toward one another on a straight track, are 300 m
apart when the engineers on both trains become aware of the impending
collision and hit their brakes. The eastbound train, initially moving at 98.0
km/h, slows down at 3.50 m/s2. The westbound train, initially moving at
120 km/h, slows down at 4.20 m/s2. Will the trains stop before colliding? If
so, what is the distance between them once they stop? If not, what initial
separation would have been needed to avert a disaster?
• The cheetah is considered the fastest running animal in the
world. Cheetahs can accelerate to a speed of 20.0 m/s in 2.50 s and can
continue to accelerate to reach a top speed of 29.0 m/s. Assume the
acceleration is constant until the top speed is reached and is zero
thereafter. (a) Starting from rest, how long does it take a cheetah to reach
its top speed and how far does it travel in that time? (b) If a cheetah sees a
rabbit 120 m away, how long will it take to reach the rabbit, assuming the
rabbit moves away at a constant velocity of 2.00 m/s?