Presentation on theme: "Chapter 3: Accelerated Motion"— Presentation transcript:
1Chapter 3: Accelerated Motion Created by G. Frega
2Changing motionYou can feel the difference between uniform and nonuniform motionWhen motion changes, you feel a push or pull (a force).Ex: a Marta train coming to a sudden stopIn uniform motion, your body becomes used to it.Ex: sitting in a car on cruise control
3Acceleration Acceleration: the rate at which velocity is changing Whenever we change our state of motion, we are accelerating.Speeding upSlowing down (negative acceleration)Changing direction
4Check Your Understanding If a dog chases its tail in a circle at the same speed the whole time, is it accelerating?Yes! Even though its speed is staying constant, it is changing direction, and therefore changing its velocity. If the velocity changes, it is accelerating.
5** Δ means “change in”** a = Δv / t** Δ means “change in”**Acceleration is how quickly we are changing our velocityEx: mph per second, k/m per second, m/s2SI Unit for acceleration is m/s2AKA meters per second per second
6Check Your Understanding Suppose a car moving in a straight line steadily increases its speed each second, first from 35 to 40 km/h, then from 40 to 45 km/h, then from 45 to 50 km/h. What is its acceleration?We see that the speed increases by 5 km/h each second. The acceleration would be 5 km/h.s during each interval.
7Check Your Understanding In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/h, while a truck goes from rest to 15 km/h in a straight line. What is the acceleration of each vehicle?a = Δv / tacar = ? atruck = ?Δvcar=65–50=15 km/h Δvtruck=15-0=15 km/ht = 5s t = 5sacar = (15 km/h) / (5s) atruck = (15 km/h) / (5s)acar = 3 km/h.s atruck = 3 km/h.s
8Check Your Understanding Which undergoes a greater acceleration?Although the speeds are different, their rate of change of speed is the same…so both have the same acceleration.
9Free Fall Free fall: when an object is only affected by gravity Consider an apple falling from a tree. We know that it starts at rest and gains speed as it falls, or accelerates.Gravity causes the apple to accelerate downward and is said to be in free fall.Free fall: when an object is only affected by gravity10 m/s2 is the acceleration due to gravity.The letter g represents the acceleration due to gravity.g = 10 m/s2
10Now consider an object thrown straight up Now consider an object thrown straight up. It will continue to move straight up, then it comes back down.At the highest point, the object changes its direction and the objects instantaneous speed is 0 m/s.Whether the object is moving up or down, the acceleration of the object is always 10 m/s2.
11To find the instantaneous speed of an object falling from it’s rest position, multiply acceleration due to gravity by the elapsed time.Elapsed time: the time that has passed since the beginning of the fallv = gt
12Check Your Understanding What would the speedometer reading on a falling rock be 4.5 seconds after it drops from rest?v = gtv = ?g = 10 m/s2t = 4.5sv = (10 m/s2) (4.5s)v = 45 m/s
13How about 8 seconds? v = gt v = 80 m/s How about 15 seconds? g = 10 m/s2t = 8sv = (10 m/s2) (8s)v = 80 m/sHow about 15 seconds?t = 15sv = (10 m/s2) (15s)v = 150 m/s
14Because an object in free fall increases the rate of distance covered every second, we cannot use v =d/t.The formula for finding the distance an object falls isd = ½ gt2
15Check Your Understanding What is the distance an object falls in one second?d = ½ gt2g = 10 m/s2t = 1 sd = ½ (10)(12)d = 5 m
16Air Resistance and Free Fall All objects fall at 10 m/s2 on EarthRegardless of weight or massEx: In a vacuum, a feather and a bowling ball will hit the ground at the same time if dropped from the same hieghtA vacuum is anyway without any air (ex: outer space)Air resistance causes objects such as a coin and a feather to accelerate differently.However, air resistance less noticeably affects the motion of more massive objects like stones and baseballs.With negligible air resistance, falling objects can be considered to be in free fall.
17Velocity – Time GraphsVelocity-Time graphs show the change of velocity over an elapsed timeAKA Speed-Time graphsRemember that speed does NOT take into account directionTime is always the independent variableVelocity is always the dependent variable
18The slope of a Velocity-Time graph is equal to acceleration Slope = rise/runSlope = change in velocity / timea = Δv / tThe steeper the slope, the faster the accelerationRemember acceleration can be speeding up, slowing down, or sharp turnsA positive slope is speeding up and moving forwardA negative slope is EITHER slowing down OR moving backwardsA zero slope means that the velocity is NOT changing, meaning that the object is moving at the same speed in the same direction
19Check Your Understanding Which person(s) could be slowing down?Person C. They have a negative slope; they could be moving backwards too (there is not enough info on the graph to tell).
20Check Your Understanding Which person(s) are not accelerating?A and E. Their have a constant velocity.Which person(s) could be speeding up?B and D. They are increasing velocity each second.