Constant AccelerationLearning Targets: Today I am deriving the four constant acceleration equations and then applying them to motions of objects that are speeding up or slowing down. I know I have it if I can solve a story problem by picking one of the four equations, then performing algebra to solve for velocity, initial velocity, displacement, acceleration or time of a motion.

Deriving Equation One1. Sketch a velocity vs. time graph with constant acceleration.

a. Write the equation for the slope.

b. multiply by time

c. add vo to both sides.

2. Deriving Equation twoa. find the area under the curve from t1 to t2 such that neither time is zero.

3. Deriving Equation Threea. Write the equation for the area under the curve again.

b. Now substitute for v

Symbol Unit represents

Last Equation! (Deriving Equation 4)4. Write the equation for the slope

a. Solve for time in your equation.

b. Substitute into the equation for area under the curve(without acceleration)

c. Solve for velocity final squared.

5. Fill in the following chart.Equation Missing

variable

6. The fastest speeds traveled on land have been achieved by rocket-powered cars. The current speed record for one of these vehicles is about 1090 km/h, which is only about 160 km/h less than the speed of sound in air. A rocket car starts at rest and just reaches a speed of 1090 km/h when it passes the 20 km mark.

a. How long does it take to make the 20 km drive?

b. How long will it take the car to slow down if it goes from its maximum speed to rest in 5 km?

7. The heaviest edible mushroom ever found (the so-called “chicken of the woods”) had a mass of 45.4 kg. Suppose such a mushroom is attached to a rope and pulled horizontally along a smooth stretch of ground, so that it undergoes a constant acceleration of +0.35 m/s2. If the mushroom is initially at rest, what will its velocity be after it has been displaced +64 m?

Learning Targets: Today I am applying the four constant acceleration equations to objects that are free falling (this can mean moving upwards or downwards). I know I have it if I can solve a story problem by picking one of the four equations, then performing algebra to solve for velocity, initial velocity, displacement, acceleration or time of a motion.

8. When an object is in free fall what forces are acting on it? Does freefall only mean down?

9. What’s the acceleration due to the gravitational force on Earth? Which has a greater acceleration due to a gravitational force? A feather or a coin?

10. A ball is thrown vertically upward. While the ball is in free fall does its acceleration increase, decrease or remain constant?

11. How fast is a ball falling 1s after it is dropped?a. 5 m/sb. 10 m/sc. 15 m/sd. 20 m/se. 25 m/s

12. How fast is a ball falling 2 s after it is dropped?a. 5 m/sb. 10 m/sc. 15 m/sd. 20 m/se. 25 m/s

13. Alice throws a ball into the air. Fill in the blanks

a=-9.8m/s2

a=___

a=___ a=___

a=___

a=___

t=3s

t=2s

t=1s

t=3s

t=4s

t=5s

v=_____

v=_____

v=_____

v=_____

v=_____v=19.6 m/s

14. A person standing at the edge of a cliff throws one ball straight up and another ball straight down at the same initial speed. Neglecting air resistance, which ball strikes the ground with a greater speed? The one initially thrown_____

a. upwardb. downwardc. neither-the both hit at the same speed

15. You are throwing a ball straight up in the air. At the highest point, the ball’s a. Velocity and acceleration are zerob. Velocity is nonzero but its acceleration is zeroc. Acceleration is nonzero, but its velocity is zerod. Velocity and acceleration are both nonzero

16. A ball is thrown vertically upward with a speed of 30 m/s. How much time does it take the ball to reach the top of its path?

a. 1 sb. 2 sc. 3 sd. 4 se. 5 s

17. The tallest Sequoia sempervirens tree in California’s Redwood National Park is 111 m tall. Suppose an object is thrown downward from the top of that tree with a certain initial velocity. If the object reaches the ground in 3.80 seconds, what is the object’s initial velocity?

18. A rocket is initially at rest and is launched upwards with an acceleration of 5 m/s2 until it reaches an altitude of 800 m then the engines turn off.

a. How fast is the rocket moving when the engines turn off?

b. What is the maximum height reached by the rocket?

Pointing the way!Learning Targets: Today I am adding vectors for motions that moving right/left or up/down. I am also comparing scalar quantities to vector quantities. I know I have it if I add or subtract the parallel vectors. 2. What is a scalar?

3. What is a vector? How do you write a variable to indicate it is a vector?

4. Circle the terms below that are vectors

Displacement distance speed velocity acceleration

Time temperature mass average velocity

5. Adding parallel vectorsa. What is the total displacement?

b. What is the total displacement?

6. The water used in many fountains is recycled. For instance, a single water particle in a fountain travels through an 85 m system and then returns to the same point. What is the displacement of a water particle during one cycle?

30m

40m30m

40m

Tip

Identify if a physics quantity is a vector or scalar

Find distance or displacement given multiple displacement vectors

7. Adding Parallel vectors : Arlo throws a sphere on a bus. According to Arlo he throws a sphere with a velocity of 10 m/s (velocity of sphere relative to the bus).

a. How fast do the students on the bus say he threw the sphere (velocity of sphere relative to the bus)?

b. Alice is standing as the bus goes by with a velocity of 15 m/s to the right. How fast does Alice think the sphere is going (velocity of sphere relative to ground)?

8. Alice and Arlo canoe downstream (with the current). Their velocity relative to

the banks of the river averages 1.23 m/s. During the return trip they paddle upstream, averaging 0.67 m/s relative to the riverbank.

a. What is their paddling velocity in still water (velocity of boat relative to water)?

b. What is the velocity of the current in the river ?

c. How far do they travel down stream in an hour? Upstream?

Make sure you know the difference between velocity according to the ground, and velocity of the engines/rowing

You are expected to be able to solve for distance and/or time traveled downstream or upstream when traveling down or up a river.

9. Applying : Arlo is driving at 50 km/h, while Alice is driving at 30 km/h. They start driving at the same point. How far apart are the cars after 4 hours?

Learning Targets: Today I am adding vectors for motions that moving right/left and up/down. I know I have it if I use Pythagorean thm to add perpendicular vectors and I place them tip to tail with the resultant from the tail to the tip of the triangle. I know I have it if I only use parallel vectors in x=vt. In other words if I use a hypotenuse velocity I must use a hypotenuse displacement.

10. Adding perpendicular vectors graphically: Tip-to-TailWhat is the total displacement? What is the total distance traveled?

Now 2 dimensional!11. Arlo’s boat is heading due South (or at least that is the way it is pointed) as it crosses a wide river with a velocity of 10.0 km/h relative to the water. The river has a uniform velocity of 5.00 km/h due west. Determine the velocity of the boat with respect to an observer on the riverbank.

a. In a story problem what does it mean if you see “velocity of the boat relative to the water” or “velocity of airplane relative to the air”?

30m40m

b. In a story problem what does it mean if you see “velocity of the boat relative to shore” or “velocity of an airplane relative to ground”?

c. Draw a velocity triangle and a displacement triangle for this scenario.

d. What is the speed of the boat according to the shore?

e. How long would it take for the boat to cross a 20 km river?

f. How far downstream does Arlo end up?

12. Alice rows a boat at 8 km/h directly across a river that flows at 6 km/h.

a. What is the resultant speed of the boat?

b. How much time does it take Alice to cross the river if it is 10 km across?

c. How far downstream does Alice end up if the river is 10 km across?

Solve for time or distance when traveling across a river.

Solve for angle in order to travel straight across a river.

13. Arlo rows a boat at 8 km/h across a 10 km wide river that flows at 6 km/h west. What if Arlo is trying to get to a point directly across on the north shore? What direction should he head?

a. Could Arlo head directly across the river? Where would he end up?

b. Which general way should he head to reach his goal? Draw a velocity and a displacement triangle for this scenario.

c. What is the speed of the boat according to the shore?

d. How long would it take for the boat to cross the river?

e. Find the actual angle at which Arlo must point his boat so his final destination is directly across the river.

14. Arlo wants to go directly across a river that is flowing at 5km/h south. If his motor is 12 km/h, at what angle should he point his boat to go from the west bank to the east bank?

Learning Targets: Today I am adding multiple vectors for motions that moving right/left and up/down. I am adding vectors using the component method so that I only add vectors that are parallel to each other, then as a last step I add perpendicular vectors using Pythagorean thm. I need to watch my signs!!!

Adding Multiple Vectors!15. While Arlo plays football he runs 20 yards downfield, then cuts towards the sideline running 15 yards and finally has to cut back 4 yards catching the football. After catching the football Arlo spins around and sprints 25 yards into the end zone!

a. What is his displacement?

Be able to apply boat problems to airplanes traveling at angles to the wind.

b. What is his total distance traveled?

16. Adding vectors graphically that are not parallel or perpendicular

Tip-to-Tail

Try adding the two vectors in a different order. Does it matter?

17. Component Method for adding a bunch of vectors (VERY IMPORTANT!!!)An ant travels 2cm at a 60 degree angle. It then travels 3 cm at a 230 degree angle. Next the ant travels 5cm at 40 degrees and then finally 1cm at 350 degrees.Find the ant’s displacement.

Draw a coordinate system for each vector so that each tail is at an origin.

3m/s2m/s

Add vectors graphically (tip to tail) (this means you draw it)

Use the component method to add vectors algebraically

Algebraically determine the resultant displacement: (Watch your signs!) x-component y-component

1

2

3

4

Total

Draw the final x vector and the final y vector tip-to-tail. Find the magnitude of the resultant using the Pythagorean Theorem

Find the direction of the result using tan-1, make sure you draw the final triangle and label the hypotenuse and angle with the tail of the hypotenuse.

18. Find the sum of these four vector forces: 12 N to the right at 35 degrees above the horizontal, 31 N to the left at 55 degrees above the horizontal, 8.4 N to the left at 35 degrees below the horizontal, and 24 N to the right at 55 degrees below the horizontal.

Use the component method to add vectors algebraically

19. A man pushing a mop across a floor causes the mop to undergo two displacements. The first has a magnitude of 150 cm and makes an angle of 120 degrees with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35 degrees to the positive x axis. Find the magnitude and direction of the second displacement.