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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 • = − = −9.8 2 (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 • = 0 + • = 0 + • ∆ = • ∆ = Linear motion equations & when to use them • Constant, non-zero acceleration • Kinematics equations 1 • = 0 + ,0 + 2 same as 2 1 • = 0 + ,0 + 2 same as 2 1 ∆ = ,0 + 2 2 1 ∆ = ,0 + 2 2 • , = ,0 + • , = ,0 + = ,0 − 2 2 2 • , = ,0 − 2 ∆ = ,0 − 2 ( − 0 ) 2 2 2 • , = ,0 − 2 ∆ = ,0 − 2 ( − 0 ) • Note: when ≠ 0, then above should be ∆ = − 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?