Motion (Chapter 2) Student Learning Objectives Compare and contrast terms used to describe motion Analyze circular and parabolic motion

 Average speed is the distance covered in some amount of time.  Velocity is speed in some direction.  Up, Down  Left, Right  N, S, E, W  –, + How do speed and velocity compare? s = d t

Practice An Olympic runner completes the 100 meter dash in 11 seconds. a)What is the runner's average speed? b)How fast is this in mph?

 Scalars are quantities that indicate size, indicate a numerical value.  Vectors are quantities that indicate the size and direction.  The magnitude of a vector is a scalar; it is the size of the vector. Example: Example: 65 mph North Scalar/Vector

How is acceleration defined?  Acceleration is the change of velocity in some amount of time.  Deceleration is negative acceleration. (opposite direction of motion) a =  v t

 A car that maintains a constant speed in a straight line has zero acceleration.  The distance traveled depends on how long the object has been accelerating. d =  1/2)at 2

Practice 1) When driving through a flat curve at a constant rate of speed, is there acceleration? Explain.

More Practice 2) On the freeway, it takes 3 seconds to increase your speed from 15 mph (6.7 m/s) to 65 mph (29 m/s). a)What is the average acceleration? b)If the car continues to accelerate, at the same rate, for another 1.5 seconds, what will the final velocity be? c)How far will the car have traveled during the 4.5 seconds of acceleration?

What causes vertical acceleration?  Objects are accelerated downward because of gravity.  The gravitational pull from the Earth is the same on all objects, so the downward acceleration is the same on all objects, 9.81 m/s 2.  Any difference in the net acceleration is due to air resistance.

Practice 1) I toss a ball upward and it returns to my hand. What is the ball’s rate of acceleration if there is no air resistance? a)Just after the ball leaves my hand? b)At the top of the trajectory? c)Just before the ball hits the ground?

More Practice 2)Professional cliff divers fall from a cliff into the sea. a)If the dive takes 2.7 seconds, what is the distance they fall? b)What would be the speed of the diver as the diver enters the water?

What is terminal velocity?  An object in free fall is only affected by gravity (no air resistance).  Air resistance provides acceleration upward.  Terminal velocity occurs when air resistance balances gravity. Surface Area Speed

What causes circular motion?  Objects move in a straight line, unless an unbalanced force changes the motion.  In circular motion, a centripetal force (“center-seeking” force) causes a constant change in motion, a constant change in direction. a c = v 2 r F c = ma c

Practice 1) Describe some examples of centripetal motion.

More Practice 2) An object is circling two times every second at the end of an 8 cm long string. a)Determine how to calculate the velocity, and calculate it. (Hint: what is the distance?) b)Calculate the centripetal acceleration. c)Calculate the amount of centripetal force on a 0.5 kg object.

Why does a projectile have a parabolic trajectory?  The addition of the horizontal velocity and the vertical acceleration due to gravity results in a curved path.

 A projectile's motion in x does not affect its motion in y! (and vice versa) Why?  Velocity in x is constant if there is no air resistance. Why? Why?  Velocity in y changes. Why?

 A projectile will fall a vertical distance (y) each second after reaching maximum height.  The range (x) of a projectile relative to the horizontal plane depends on the object’s horizontal velocity and time of flight. x = vt y =  1/2)gt 2

Practice 1) At what angle relative to the ground should a football be thrown to have the greatest horizontal range? 2) What are some examples of projectile motion that you have observed?

More Practice 3) A player throws a baseball parallel to the ground with a horizontal velocity of 90 mph (40 m/s). Assume no air resistance. a)What is the direction of the acceleration? b)Does the horizontal speed change? Does the vertical speed change? c)What is the horizontal speed the instant before the ball hits the ground? d)If there was no gravity, what would be the path of the ball? Why?

The Range e) What is the maximum horizontal range of the baseball if it is released from a height of 1.5 meters at 40 m/s?