Physics 12 - Kinematics

Review

Speed vs. Velocity?

Rolling ball……..our first equation

Example

A car travels 60. km in 30. min, then turns around and travels 30. in ½ hour.

What is the car’s speed over the entire trip? In km/hr? In m/s?

What is the car’s average velocity in m/s over the trip?

Acceleration

A change in velocity (speed or direction!!)Rate of change of velocity (a=∆v/∆t)

2 important quantities to identify from a v-t graph:1. The slope of a line (gives us acceleration)2. The area under a curve (gives us

displacement)

The other important equations…..

vf = vi + at

d = ½ (vf + vi)t

vf2 = vi

2 + 2ad

d = vit + ½ at2

An object accelerates uniformly from rest. If the final velocity of the object after 4.7 s is 15 m/s east, what is it’s displacement?

Concept Questions…….

1. A person initially at point P in the illustration stays there a moment and then moves along the axis to Q and stays there a moment. She then runs quickly to R, stays there a moment, and then strolls slowly back to P. Which of the position vs. time graphs below correctly represents this motion?

2. An object goes from one point in space to another. After it arrives at its destination, its displacement is: a. either greater than or equal to b. always greater than c. always equal to d. either smaller than or equal to e. always smaller than f. either smaller or larger

than the distance it traveled.

3. A marathon runner runs at a steady 15 km/hr. When the runner is 7.5 km from the finish, a bird begins flying from the runner to the finish at 30 km/hr. When the bird reaches the finish line, it turns around and flies back to the runner, and then turns around again, repeating the back-and-forth trips until the runner reaches the finish line. How many kilometers does the bird travel? a. 10 km b. 15 km c. 20 km d. 30 km

4. A train car moves along a long straight track. The graph shows the position as a function of time for this train. The graph shows that the train:

a. speeds up all the time. b. slows down all the time. c. speeds up part of the time and slows down

part of the time. d. moves at a constant velocity

5. The graph shows position as a function of time for two trains running on parallel tracks. Which is true:

a. At time tB, both trains have the same velocity.

b. Both trains speed up all the time. c. Both trains have the same velocity at some

time before tB.

d. Somewhere on the graph, both trains have the same acceleration.

Free Fall

Gravity…..

g = +9.80 m/s2

or

g = -9.80 m/s2

You hold a ball in your hand at a fixed height and release it. Its initial velocity is a. up b. zero c. down

You hold a ball in your hand at a fixed height and release it. Its initial acceleration is a. up b. zero c. down

4. If you drop an object in the absence of air resistance, it accelerates downward at 9.8 m/s2. If, instead, you throw it downward, its downward acceleration after release is a. less than 9.8 m/s2. b. 9.8 m/s2. c. more than 9.8 m/s2.

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

5. 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, the ball to hit the ground below the cliff with the greater speed is the one initially thrown

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

Example….

A rock is thrown with a velocity of 5.0 m/s downward from a cliff of height 60. m.

How long does it take the rock to hit the ground?

What is the rock’s speed when it hits the ground?

Example

An object is launched directly upward with a velocity of 7.9 m/s.

a. How long does it take to reach the top of the trajectory?

b. What is the object’s velocity at t = 0.5 s? t = 3. s?c. What is the object’s hang time ( total time in the

air)?d. What is the max height reached?

Projectile Motion

Motion though the air without propulsion

Examples:

Part 1.Motion of Objects Projected Horizontally

v0

x

y

x

y

x

y

x

y

x

y

x

y

•Acceleration is constant (g = 9.80 m/s2 [downward] )

•vx is constant

•Horizontal and vertical motions are independent of each other, but they have a common time

g = -9.81m/s2

ANALYSIS OF MOTION

QUESTIONS:

• What is the trajectory?

• What is the total time of the motion?

• What is the horizontal range?

• What is the final velocity?

Question:

A ball is launched horizontally from the top of a 50.0 m tall cliff with a velocity of 20.0 m/s.

Find: a)Flight timeb)Rangec) Final Velocity

Part 2.Motion of objects projected at an angle

What launch angle will produce the same range as….

a) 75o b) 52o c) 40o

x

y

• Acceleration is constant (g = -9.80 m/s2 [downward] )

• vx is constant

• Horizontal and vertical motions are independent of each other, but they have a common time

• Initial velocity must be broken into it’s components!

Equations of motion:

XUniform motion

YAccelerated motion

ACCELERATION ax = 0 ay = g = -9.81 m/s2

VELOCITY vx = vi cos Θ vy = vi sin Θ + g t

DISPLACEMENT x = vi t cos Θ y = vi t sin Θ + ½ g t2

Question:

A projectile is launched with a velocity of 100.0 m/s [35.0o N of E]

Find:a)Time to the top b)Maximum heightc)Total flight timed)Rangee)What angle will produce the same range?

Answers….

a) 5.85 sb) 168 Mc) 11.7 sd) 958 me) 55o

Projectile Activity

Question:

A projectile is launched from the top of a 60.0 m building with a velocity of 50.0 m/s at an angle of 30.0o with the horizontal.

Find:a)Time to the top b)Maximum height (relative to the ground)c)Total flight timed)Range

Relative Velocity

Always need a reference point

Example: VAB

Stated as: “Velocity of Object A relative to Object B”

The Physics Classroom

Riverboats and Plane Problems

vresult = vboat + vwater

or

vresult = vplane + vwind

1. A plane can travel with a speed of 80. km/hr with respect to the air. Determine the resultant speed (aka ‘ground speed’) of the plane if it encounters a 21 km/hr cross wind.

2. A motorboat traveling 6 m/s East across a river encounters a current traveling 3.8 m/s, South.

a. What is the resultant velocity of the motor boat?

b. If the width of the river is 120. meters wide, then how much time does it take the boat to travel shore to shore?

c. What distance downstream does the boat reach the opposite shore?

3. An airplane flies west at 300. km/hr. Wind blows North East at 100. km/hr. What is the plane’s velocity relative to the ground?

3. An airplane flies west at 300. km/hr. Wind blows from the North East at 100. km/hr. What is the planes velocity relative to the ground?

Remember: vresult = vplane + vwind

Set up a table:

Vector X Component Y-Component

Plane

Wind

Result

Answers…

R = 239.9 km/hr [17o N of W]

The challenger….

4. A pilot wishes to fly to a city that is directly 752 km East of her position. Her air speed is 195 km/h and there is a wind from the north of 73 km/h.

a) What direction should she point the plane?b) What will be her ground speed?c) How long will it take to get there?

Answers…

a) Θ = 22o N of Eb) 195cos22o = 180.8 km/hrc) t = 4.16 hr