Relative Motion AP Physics 1

Representing 1D motion pg 32 horizontally vertically

1D Velocity Horizontal Vertical

Compare to Slope Average Velocity vx avg =

Uniform Motion Be Careful !!! This equation only works for Uniform Motion (i.e. constant velocity) Good for when the initial position ≠ zero Alternate form: xf – xi = vx(tf – ti)

Football A wide receiver caught the pass on the opponents 40 yard line and ran the the 10 yard line where he was tackled. If he ran with the football for 3 seconds, what was his average velocity?

Position, Velocity, Acceleration

Acceleration Acceleration is velocity divided by time

Velocity equation For an object with constant acceleration

Change in Velocity A car traveling at +75 km/h slows down to +25 km/h in 4.3 s. What was the acceleration? What does this acceleration mean? How would your answer change if the car was traveling in a negative direction?

Position Equation For an object with constant acceleration

Bell Ringer: Change in Speed A car travels 125 m in 9.3s while accelerating from an initial speed of 33.0km/h. What is the car’s final speed?

Position equation A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s2. Determine the time for the feather to fall to the surface of the moon. Problem 5: http://www.physicsclassroom.com/class/1DKin/Lesson-6/Sample-Problems-and-Solutions

Position equation A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled. Problem 4: http://www.physicsclassroom.com/class/1DKin/Lesson-6/Sample-Problems-and-Solutions

Example: Calculate the impact speed with the water after falling from 40ft above the water, from rest. Assuming he stops in a depth of 12inches of water, determine his acceleration, assuming it to be constant .

EXAMPLE 2 As a part of a movie stunt a stunt man hangs from the bottom of an elevator that is rising at a steady rate of 1.10m/s.  The man lets go of the elevator and freefalls for 1.50s before being caught by the end of a rope that is attached to the bottom of the elevator.  (a) Calculate the velocity of the man at the instant he is caught by the rope.   a) -13.6 m/s b) 11m - find disp of man + dist of elevator in 1.5s (b) How long is the rope?

EXAMPLE 3 An honors physics student stands at the edge of a cliff that is 36m high. He throws a water balloon straight up at 12.5m/s so that it just misses the edge of the cliff on the way down. Determine velocity of balloon as it strikes ground below (many ways to solve) 17

Collaborate with person next to you to answer following questions: Three students are standing side-by-side next to the railing on a fifth floor balcony. Simultaneously, the three students release their pennies.  One student drops a penny to the ground below. The second student tosses penny straight downwards at 15 m/s while third student tosses penny straight upwards at 15 m/s. Assume freefall. a) Which penny or pennies strike(s) ground first? b) Which penny or pennies strike(s) ground last? c) Which penny or pennies strike(s) the ground with the greatest final velocity? d) Which penny or pennies strike(s) the ground with the greatest acceleration?

Bell Ringer: Change in Speed A drag racer travels 125 m in 9.3s while accelerating. What is the car’s final acceleration?

Relating Velocity and Displacement For an object with constant acceleration Velocity with constant acceleration

Change in Velocity The brakes of a car whose initial velocity is 30. m/s are applied and the car receives an acceleration of -2.0 m/s2. A)How far will it have gone when its velocity has decreased to 15 m/s? B)How far will it have gone when it has come to a stop?

Planes Two planes take off from the same airport at the same time. One plane has an air speed of 500 mph and a bearing of 280°, and one plane has an air speed of 600 mph and a bearing of 35°. After 2 hours, how far apart are the planes? A. 929.29 miles B. 1194.03 miles C. 1858.57 miles

v-t graphs – part 2

Graphical Analysis of Motion (2) velocity-time graph: Describes the velocity of object during a given time period.

Acceleration Acceleration is a changing Velocity (either magnitude and/or direction) Change in velocity Change in time Units?

Constant Acceleration Constant acceleration implies what about velocity? Constant acceleration or deceleration implies what about distance? Acceleration of zero implies what about the velocity? 27

Negative acceleration vs Positive acceleration: Both can equate to slowing down. When sign of acceleration matches sign of velocity, object speeds up in direction of that sign. When signs oppose, object slows down in direction of ‘v’.

Velocity equation For an object with constant acceleration

Position Equation For an object with constant acceleration

Bell Ringer: Change in Speed A car travels 125 m in 9.3s while accelerating from an initial speed of 33.0km/h. What is the car’s final speed?

Position equation A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s2. Determine the time for the feather to fall to the surface of the moon. Problem 5: http://www.physicsclassroom.com/class/1DKin/Lesson-6/Sample-Problems-and-Solutions

Position equation A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled. Problem 4: http://www.physicsclassroom.com/class/1DKin/Lesson-6/Sample-Problems-and-Solutions

Relating Velocity and Displacement For an object with constant acceleration

Relating Velocity and Displacement A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The bullet penetrates for a distance of 0.0621 m. Determine the acceleration of the bullet while moving into the clay. (Assume a uniform acceleration.) Problem 15; http://www.physicsclassroom.com/class/1DKin/Lesson-6/Sample-Problems-and-Solutions

Relating Velocity and Displacement An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is likely to be 3 m/s^2. The takeoff speed for this plane will be 65 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway? Problem 8; http://www.physicsclassroom.com/class/1DKin/Lesson-6/Sample-Problems-and-Solutions

Relating Velocity and Displacement A baseball is popped straight up into the air and has a hang-time of 6.25 s. Determine the height to which the ball rises before it reaches its peak. (Hint: the time to rise to the peak is one-half the total hang-time.) Problem 13; http://www.physicsclassroom.com/class/1DKin/Lesson-6/Sample-Problems-and-Solutions

EXAMPLE While driving along at 20m/s, you notice the light up ahead turns red (110m away). Assuming you have a reaction time of 0.5s, a) How far from the light are you when you begin to apply the brakes? b) What constant acceleration will bring you to rest at the light?

EXAMPLE 2 A car starts from rest at a stop sign. It accelerates uniformly at 4.0m/s2 for 6.0s, coasts for 2.0s, and then slows down at 3.0m/s2 for the next stop sign. a) How far apart are the stop signs? b) Determine the maximum velocity during the trip.

We will only deal with constant accelerations. a vs t graph a t We will only deal with constant accelerations.

EXAMPLE 1 A ball is thrown upward with an initial speed of 15.0m/s Assume negligible air resistance.  a) Find the maximum height attained by the ball. b) How much time does it take to reach the apex?  c) Determine the velocity 2.2s into flight.

Posters – 6 equations For each poster Show equation What information is needed to use this equation? What type of problem can this equation be useful? Give examples

Uniform Motion Uniform Motion

Position Equation with Constant Acceleration x- and y- directions are independent of the other

Average Acceleration Average acceleration v = at t = v/a

Velocity and Constant Acceleration

Velocity Equation Velocity equation

Average Velocity Average velocity d=vt, v=d/t, t=d/v