Example A car travels 60. km in 30. min, then turns around and travels 30. in ½ hour. What is the cars speed over the entire trip? In km/hr? In m/s? What is the cars 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….. v f = v i + at d = ½ (v f + v i )t v f 2 = v i 2 + 2ad d = v i t + ½ at 2
An object accelerates uniformly from rest. If the final velocity of the object after 4.7 s is 15 m/s east, what is its displacement?
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 t B, 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 t B. d.Somewhere on the graph, both trains have the same acceleration.
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/s 2. If, instead, you throw it downward, its downward acceleration after release is a.less than 9.8 m/s 2. b.9.8 m/s 2. c.more than 9.8 m/s 2.
You are throwing a ball straight up in the air. At the highest point, the ball's a.velocity and acceleration are zero b.velocity is nonzero but its acceleration is zero c.acceleration is nonzero, but its velocity is zero d.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.upward b.downward c.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 rocks 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 objects velocity at t = 0.5 s? t = 3. s? c.What is the objects 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
x y Acceleration is constant (g = 9.80 m/s 2 [downward] ) v x is constant Horizontal and vertical motions are independent of each other, but they have a common time g = -9.81m/s 2
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 time b)Range c)Final Velocity
Part 2. Motion of objects projected at an angle
What launch angle will produce the same range as…. a) 75 o b) 52 o c) 40 o
x y Acceleration is constant (g = - 9.80 m/s 2 [downward] ) v x is constant Horizontal and vertical motions are independent of each other, but they have a common time Initial velocity must be broken into its components!
Equations of motion: X Uniform motion Y Accelerated motion ACCELERATION a x = 0a y = g = -9.81 m/s 2 VELOCITY v x = v i cos Θv y = v i sin Θ + g t DISPLACEMENT x = v i t cos Θy = v i t sin Θ + ½ g t 2
Question: A projectile is launched with a velocity of 100.0 m/s [35.0 o N of E] Find: a)Time to the top b)Maximum height c)Total flight time d)Range e)What angle will produce the same range?
Answers…. a)5.85 s b)168 M c)11.7 s d)958 m e)55 o
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 30.0 o with the horizontal. Find: a)Time to the top b)Maximum height (relative to the ground) c)Total flight time d)Range
Relative Velocity Always need a reference point Example: V AB Stated as: Velocity of Object A relative to Object B
Riverboats and Plane Problems v result = v boat + v water or v result = v plane + v wind
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 planes 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: v result = v plane + v wind Set up a table: VectorX ComponentY-Component Plane Wind Result
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 = 22 o N of E b)195cos22 o = 180.8 km/hr c)t = 4.16 hr