3 Chapter 2 Review Quantity Symbol Unit Position m Displacement m DistancemTimesVelocitySpeed
4 Acceleration How fast is your position changing? VelocityHow fast is your velocity changing?AccelerationBoth velocity and acceleration are vector quantities with both direction and magnitude.But velocity and acceleration are two different concepts.
6 Example (64-6)A race car’s velocity increases from 4.0 m/s to 36 m/s over a 4.0-s time interval. What is its average acceleration?
7 What does the negative acceleration mean? Opposite to + direction.Practice (64-9)What direction has been defined as the positive direction? Direction of motion.A bus is moving at 25 m/s when the driver steps on the brakes and brings the bus to a stop in 3.0s.What is the average acceleration of the bus while braking?
8 Instantaneous Acceleration Instantaneous acceleration is average acceleration when the time interval becomes very, very small.On a velocity-time graph, the instantaneous acceleration at any time is given by the slope of the line tangent to the curve at that time.Draw line tangent to curve at given time.Locate two points on tangent line and find coordinates. (t1, v1) and (t2, v2)Find slope using equation
9 Instantaneous acceleration and slope v (m/s)Draw tangent line at 3 s.60Two points are _______ and ___________.(1.8s, 0)50(6.0s, 35m/s)40•3020•10•123456t (s)at=3s= 8.3 m/s2What is the acceleration at 3 s?a3s= 8.3 m/s2
10 Draw a velocity-time graph for an object whose velocity is constantly decreasing from 10 m/s at t = 0.0s to –10 m/s at t = 2.0s. Assume it has constant acceleration.What is its average acceleration between 0.0s and 2.0s?What is its acceleration when its velocity is 0 m/s?Examplea)v (m/s)t (s)•1012•-10
11 Negative acceleration Acceleration is a vector quantity.Negative sign of acceleration indicates direction only.Negative acceleration does not necessarily mean slowing downThink of acceleration as a push in a direction (though not exactly correct.)
12 Speeding Up or Slowing down v:+v:+ speeding up slowing downa:+a:-v:-v:- speeding up slowing downa:-a:+v and a are in the same direction (or have the same sign) ___________speeding upv and a are in the opposite direction (or have the opposite signs) ____________slowing down
13 Constant acceleration motion a = constant. Also, let ti = 0:
14 ExampleAn airplane starts from rest and accelerates at a constant m/s2 for 30.0 s before leaving the ground. What is its displacement during this time?
15 A driver brings a car traveling at +22 m/s to a full stop in 2. 0 s A driver brings a car traveling at +22 m/s to a full stop in 2.0 s. Assume its acceleration is constant.What is the car’s acceleration?How far does it travel before stopping?PracticeDefine the direction of motion to be the + directionWhat does the negative mean?
17 Practice 4: An airplane accelerates from a velocity of 21 m/s at the constant rate of 3.0 m/s2 over +535 m. What is its final velocity?
18 Free-Fall MotionAssume no air resistance. (Valid when speed is not too fast.)a = g, downward (g = 9.8 m/s2)Acceleration can be positive or negative, depending on what we define as the positive direction.g is always a positive number, equivalent to 9.81 m/s2.Does not matter if the object is on its way up, on its way down, or at the very top.g is acceleration due to gravity (It is not gravity.) g does not depend on mass of object.
19 Signs of v and a v = 0 a: - v = 0 a: + v: + a: - v: - a: + v: a: v: - Define: up = +Define: down = +
20 Free-Fall motion equations These equation are valid only when downward is defined as the positive direction.Not valid when upward is defined as the positive direction. (Must replace every g with –g.)No need to remember these equations.
21 Terms to rememberDrop, release initial velocity is zero with respect to hand. (Initial means at the moment right after it leaves hand.)Throw initial velocity is not zero with respect to hand.When it hits the ground right before it hits the ground.Rest v = 0At top of ascent v = 0
22 Example 5 A man falls 1.0 m to the floor. How long does the fall take? How fast is he going when he hits the floor?Example 5Define downward as the positive direction, then a = g
23 A pitcher throws a baseball straight up with an initial speed of 27 m/s. How long does it take the ball to reach its highest point?How high does the ball rise above its release point?PracticeDefine upward as the positive direction, then a = -g
24 You throw a beanbag in the air and someone catches it 2 You throw a beanbag in the air and someone catches it 2.2 s later at its highest point.How high did it go?What was its initial velocity?PracticeDefine upward as the positive direction, then a = -g, let d = 0 at hand.
25 Position, Velocity, and acceleration Graphs Position (vs. Time) graphv = sloped = Area under curveVelocity (vs. Time) grapha = slopev = Area under curveAcceleration (vs. Time) graph