Uniform Accelerated Motion UAM Motion in a straight

Uniform Accelerated Motion (UAM) Motion in a straight line with constant acceleration. There are several equations of motion that can be used in this type of situation.

The Big Three

A plane lands at 300 m/s. It stops at the end of a 500 m long runway. a) Find its acceleration b) How much time did it take to stop? How do we solve UAM problems? All UAM problems involve 5 quantities. You MUST be given 3 of them to find the others.

1) 2) 3) 4) 5) List all 5 quantities symbols. Fill in known quantities Identify unknown quantity Pick the pertinent equation Solve

A plane lands at 300 m/s. It stops at the end of a 500 m long runway. a) Find its acceleration vi = vf = a= d= t=

A plane lands at 300 m/s. It stops at the end of a 500 m long runway. b) vi = vf = a= d= t= How much time did it take to stop?

A rocket leaves a space station on its way to explore Uranus. If it starts from rest and accelerates at a rate of 25 m/s 2, how long will it take to move 20 km? vi = vf = a= d= t= t= 40 s

Late for his fantasy football draft, Mr. Sawyer starts from rest and accelerates at a rate of 10 m/s 2. After 5 seconds he is spotted by a policeman. How far did he travel before he was spotted? How fast was he going? vi = vf = a= d= t= d = 125 m vf = 50 m/s

A chaihuahua is initially walking at 1 m/s when he spots a fire hydrant off in the distance. In need of relief, the dog accelerates at a rate of 2 m/s 2 until it reaches the hydrant 10 seconds later. How far did the dog run before it could visit the hydrant? vi = vf = a= d= t= d = 110 m

A runaway physics experiment is traveling at 10 m/s to the right and accelerating uniformly at 2. 5 m/s 2 to the right. If the total displacement is 15 m, what is the final velocity? vi = vf = a= d= t= vf = 13. 2 m/s

An air conditioning unit is slid toward a student teacher’s head with an initial velocity of 20 m/s. It decelerates uniformly at 6 m/s 2 while it slides the 25 m across the floor. What is the machine’s final velocity? vi = vf = a= d= t= vf = 10 m/s

Toonces the driving cat starts from rest and travels 100 km in 2 hours while accelerating uniformly. What was his acceleration in m/s 2? vi = vf = a= d= t= a = 0. 0039 m/s 2

A car decelerates at 3 m/s 2 to a speed of 10 m/s in 60 m. How fast was it going? vi = vf = a= d= t= vi= 460 m/s

A car starts from rest and accelerates at 4 m/s 2. How much time does it take to cover a distance of 72 m?

Complete the 5 word problems. All must be done in Sesame Street format.

Free Fall The motion of an object under the influence of only gravity. For now, the effects of air resistance is ignored. Acceleration due to gravity g = - 9. 8 m/s 2 Negative means down!!!!!

Dropped means vi = 0!!!! A ball is dropped. How far does it fall in 3 s? How fast is it going after 3 s?

Apex means vf = 0!!!! A chunk of bleu cheese is thrown up at 40 m/s. How high does it go and how long does it take to return? Free fall is symmetrical!!!! Time up = time down!!!!

g = - 9. 8 m/s 2 always!!!!! Dropped means vi = 0!!!! Apex means vf = 0!!!! “When it hits the ground” does not mean v = 0!!!!! Objects cannot be thrown up with a v = 0!!!

A marsupial is shot upward from a cannon. It reaches a height of 60 m. a)What is its velocity when it leaves the cannon? b)How much time does it take to reach the apex? c)What is its velocity when it returns to the cannon? d)What kind of marsupial is it (the only American marsupial? )

Opossum

1) d = -1. 2 m a = - 1. 62 m/s 2 vi = 0 t=? d = v it + ½ a t 2 t = 1. 22 s 2) vi = 0 t=8 s a = - 9. 8 m/s 2 a) vf = ? vf = vi + at vf = - 78. 4 m/s b) d = ? d = v it + ½ a t 2 d = - 313. 6 m 3) vi = 0 vf = 73. 5 m/s a = - 9. 8 m/s 2 a) d = ? vf 2 = vi 2 + 2 a d d = 275. 6 m b) t = ? vf = vi + at t = 7. 5 s

4) vi = 0 d = -1. 20 m a = - 9. 8 m/s 2 a) vf = ? vf 2 = vi 2 + 2 a d vf = 4. 85 m/s b) vf = 0 d = 1. 00 m a = - 9. 8 m/s 2 vi = ? vf 2 = vi 2 + 2 a d vi = 4. 42 m/s c) vi = - 4. 85 m/s vi = 4. 42 m/s t = 0. 10 s a) a = ? vf = vi + at a = 927 m/s 2

The Effects of air resistance Air resistance is a force that slows objects down caused by movement through air.

Air resistance depends on two factors: a)Shape of the object (how aerodynamic it is) b)How fast it is going (gets stronger as the object moves faster)

Terminal velocity A falling object will reach a constant speed due to air resistance and will fall at this terminal velocity. After about 15 seconds, a skydiver will reach a speed of around 120 mph and will fall at this constant speed.

Terminal velocity can be altered by changing the shape of the object. A skydiver will spread his body out to slow his fall. A parachute slows him even further.

A student is determined to test the law of gravity for himself and walks off a skyscraper 300 m high, stopwatch in hand.

Five seconds later, Superman arrives at the scene and dives off the roof to save the student.

What must Superman’s initial velocity be for him to catch the student just before the ground is reached? (Assume that Superman’s acceleration is that of any free -falling body. )

If the height of the skyscraper is less that some minimum value, even Superman can’t save the student. What is this minimum height?

ARod is projected upward from the top of a 50 m high cliff with an initial speed of 40 m/s. a) How high does he go? b) What is his velocity after 6 seconds? c) What is his velocity at the apex? d) What is his acceleration at the apex? e) He misses the cliff on the way down. What is his velocity when he hits the ground 50 m BELOW the cliff? f) How much time does this take?

At the instant a traffic light turns green, a car that had been waiting starts ahead with an acceleration of 2 m/s 2. At the same instant a truck moving with a constant speed of 10 m/s passes the car. a)How far beyond its starting points will the car overtake the truck? b)How fast will it be travelling?

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck accelerates at 2 m/s 2 and the car accelerates at 3 m/s 2. The automobile overtakes the truck after the truck has moved 75 m. a) How long does it take the car to catch the truck b) How far was the car behind the truck initially?

A student is running to catch the campus shuttle bus, which is stopped at the bus stop. The student is running at a constant velocity of 6 m/s; she cannot run any faster. When the student is still 80 m from the bus, it starts to pull away. The bus moves with a constant acceleration of 0. 2 m/s 2. For how much time and how far will the student have to run before she overtakes the bus?

In order to determine the depth of a well, a physics student drops a stone in the well and waits to hear the splash; he hears it 3. 13 s later. How deep is the well? Assume the speed of sound is a constant 1100 ft/s.