Presentation on theme: "Chapter 10: Motion 10.1 An object in motion changes position"— Presentation transcript:
1Chapter 10: Motion 10.1 An object in motion changes position 10.2 Speed measures how fast position changes10.3 Acceleration measures how fast velocity changes
210.3 Acceleration measures how fast velocity changes Before, you learned:Speed describes how far an object travels in a given timeVelocity is a measure of the speed and direction of motionNow, you will learn:How acceleration is related to velocityHow to calculate acceleration
3Speed and direction can change with time Throw a ball in the air, it comes back down, bounces on the ground - the speed and direction are constantly changingYou can find out an object’s position change during a certain amount of time if you know the velocityCan also measure how an object’s velocity changes with time:Acceleration: The rate at which velocity change with time – how quickly velocity is changingConstant 30 km/hr trip: acceleration = ?
4AccelerationTypically “speeding up”, but can be any change in velocityA car slowing down is acceleratingA runner turning a corner, yet at constant speed, IS accelerating – direction of velocity has changedA vector - size & direction…a change being slow down, speed up, or turn
5Acceleration 1. Acceleration in the same direction as motion The speed of the object increases2. Acceleration in the opposite direction of motionThe speed of the object decreases3. Acceleration at a right angle to motionThe direction of motion changes (speed can stay the same)
6Acceleration can be calculated from velocity and time A race: in 1 s, you go from standing still to running 6 m/s, while your classmate goes from 0 m/s to 3 m/sHow did velocity change over time?Compare the initial and final velocitiesKnow the time interval over which the velocity changedAcceleration = ??What if classmate goes from 3 to 6 m/s in 1 s?As long as the velocity is increased by 3 m/s, the acceleration remains the same.
7Calculating Acceleration Know the initial and final velocities, and the time intervalAcceleration (m/s2) = [final velocity (m/s) – initial velocity (m/s)]time (s)a = vfinal – vinitial m/s2 = (m/s – m/s) = (m - m) * 1t s s s s1. A train traveling at 10 m/s slows down to a complete stop in 20 s. What is the acceleration of the train?2. Man walking 0.5 m/s accelerates to 0.6 m/s in 1 s.You know:You want to know:Formula:Substitute:Calculate:Check your units:
8Calculating Acceleration Know the initial and final velocities, and the time intervalAcceleration (m/s2) = [final velocity (m/s) – initial velocity (m/s)]time (s)a = vfinal – vinitial m/s2 = m/s – m/s = (m - m) * 1t s s s sA man walking 0.5 m/s accelerates to 0.6 m/s in 1 s. What is his acceleration?You know:You want to know:Formula:Substitute:Calculate:Check your units:
9Acceleration over Time Even a very small acceleration can lead to great speeds if given enough timeDeep Space 1: acceleration < m/s2over 20 months speed is increased by 4500 m/s (10,000 mi/h)Although the thrust from the engine is less pressure than the weight of a single sheet of paper in the hand, each day it will add between 15 mph to 20 mph to the probe's speed.In 300 days it will have accelerated the Deep Space One by 60,000 mph
10Velocity-time graphs Acceleration = velocity / time The distance an object travels depends on its velocity
12Velocity Time GraphCalculate how far the ball traveled: Distance = velocity * timeV= 200cm/s, t = .2s D = 40 cm (A = bxh area under the “curve”)
13Velocity Time GraphAcceleration (m/s2) = [final velocity (m/s) – initial velocity (m/s)]time (s)Question: Consider the motion of the object whose velocity-time graph is given in the diagram.What is the acceleration of the object between times and ?What is the acceleration of the object between times and ?What is the net displacement of the object between times and ?area