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## Constant Speed & Acceleration

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**Inertial Reference Frame**Defined as the perspective from which a system is being observed Usually define up and right as positive and down and left as negative**Distance**Definition - the total length an object travels to reach its destination How to measure – measuring tape, meter stick, laser range finder Units – meters also: cm, feet, miles, km d Start Finish Middle**Displacement**Definition - change in position of an object How to measure – measuring tape, meter stick, laser range finder Units – meters also: cm, feet, miles, km Δx Start Finish Middle**Time (t)**Definition – the interval between events Measured – using clocks, atomic vibrations (really small), revolution of earth (big) Units – seconds also: (minutes, hours, years)**Speed (s)**Definition – the rate at which distance changes with time (how fast are you going) Units – m/s or: mi/hr or km/hr Measured – measured indirectly using lasers or Doppler effect. Calculated not measured directly Formula speed = distance / time**Velocity**Definition – vector which shows the rate at which displacement changes with time Units – m/s or: mi/hr or km/hr Measured – same as speed Formula v = Δx Δt**Being safe…**Determining a safe following distance with reaction time**Displacement v. Time Graph**Can give you: • Change in position (displacement) after certain time • Time it takes to change positions • The average velocity for trip • The instantaneous velocity of a point**Teacher Example C**How long will it take for a car moving at 20 m/s to travel 1500 m?**Student Example C**How far will a car traveling at 60 m/s go if it travels for 12 seconds?**Teacher Example B**Calculate the time in standard units of a car that travels 65 m.p.h. for 34 km**Student Example B**Calculate the distance in standard units of a car that travels 55 km/ hour for 35 minutes**Teacher Example B**A man walks 10 m down the street then remembers he forgot his book at home. If his house is 100 m away from his destination and he takes 20 seconds to complete the trip what is his velocity?**Student Example B**Calculate the average velocity and average speed of a car that travels 1800 m due east and then 2400 m due west in 125 seconds**Teacher Example A**Car A is initially moving at 15 m/s in the right lane of the highway. Car B is moving at 22 m/s in the left lane. If Car B is initially behind Car A by 50 m then how long will it take Car B to pass Car A**Student Example A**Car A is initially moving at 15 m/s in the left lane of the highway. Car B is moving at 22 m/s in the left lane moving the opposite direction. If they see each other at the top of their respective hills and it takes 10 seconds for them to pass then how far apart are the hills**Teacher Example B**• What will the motion be at 5 seconds?**Student Example B**What is the time required for the object to reach 27 meters?**Teacher Example A**Two cars are separated by a distance of 1000 m. If both cars are travelling in the same direction then what is the velocity of Car B if Car B catches Car A after 50 seconds and Car A is known to be travelling 20 m/s**Student Example A**Two cars are 1500 m apart heading toward each other. How long would it take for the cars to pass each other if Car A travels at 20 m/s and Car B travels at 50 m/s?**Key Variables - Review**Velocity – vector indicating the rate at which displacement changes with time. initial velocity (vi) – final velocity (vf) -**Key Variable - New**Definition – vector indicating the rate of change in velocity. Measured – indirectly using velocity, distance and time or using an ACCELEROMETER Units – m/s^2 almost never ft/s^2**Key equation**• Change in velocity a = Δv t**Velocity v. Time Graph**Can show: • Instantaneous velocity at given time • Time it takes to reach a certain velocity • Acceleration of an object • Displacement of the object**Acceleration in a Velocity v. Time Graph**Slope will tell rate of acceleration**Teacher Example C**Pick three ways you can safely accelerate a car and describe how each is classified as acceleration.**Student Example C**Pick an activity other than driving and show three ways that you accelerate in that activity and why you would accelerate.**Teacher Example B**Calculate the acceleration of a car that speeds up from rest to a velocity of 34 m/s east in 4 seconds**Student Example B**Calculate the final velocity of a car if it travels at 4 m/s west and accelerates at 1.2 m/s2 for 13 seconds**Teacher Example A**Determine the time it takes for a car to accelerate from 20 to 60 mph if it can accelerate at 8.6 m/s2**Student Example A**• Determine the final velocity if a car accelerates from 5 mph at 8.0 m/s^2 for 1 minute.**Student Example C**• What is the acceleration of the car?**Teacher Example B**What is the velocity at 4 m/s?**Teacher Example A**What is the displacement at four seconds?**Student Example A**What is the total displacement of the object?**4 Kinematics Motion Equations**Δx = (1/2)(vi + vf)Δt vf = vi + aΔt Δx = viΔt+ (1/2)aΔt2 vf2 = vi2 + 2aΔx**Which equation do you use when?**• All equations have 4 variables in them Δt = vi= vf = a = Δx =**Teacher Example - C**Given vi, vf and displacement but trying to solve for acceleration, what would the working equation be?**Student Example - C**Given vi, time and displacement but trying to solve for acceleration, what would the working equation be?**Teacher Example - B**Determine the final velocity of a plane that is initially at 200 m/s and has a negative acceleration of 5.0 m/s2**Teacher Example - B**Determine the final velocity of a plane that is initially at rest and accelerates at 10 m/s2 over the course of 25 seconds