Speed, Velocity and Acceleration

Speed Speed is the distance traveled divided by time. Speed= distance traveled/time taken

Velocity and Speed In physics we distinguish between speed and velocity: Speed refers to how quickly an object moves (a scalar quantity). Velocity is defined as speed in a given direction or rate of change of position (displacement over time). v = x/t

Velocity Velocity refers to both the speed and direction of motion of an object (a vector quantity). Two objects travelling with the same speed but in different directions have different velocities Motion at constant velocity means that both the speed and direction of an object do not change. In a car, we can change the velocity three ways: gas pedal to speed up, brake to slow down or steering wheel to change direction

Velocity Velocity is the distance traveled in a given direction( or displacement) divided by the time taken. Velocity= displacement time taken

Velocity Questions How far does Bob run if he maintains an average velocity of 3 m/s for 10 s? List three ways you can change the velocity of your car. Is it possible to go around a corner without changing velocity? Explain. One car is going 25 miles/hr north, another car is going 25 miles/hr south. Do they have the same velocity? Explain.

Acceleration For its velocity to change, an object must accelerate. An object accelerates whenever its speed or direction or both change. Acceleration may be positive (increasing speed) or negative (decreasing speed). Acceleration is a measure of how quickly the velocity changes: a = Dv/t =(final velocity-initial velocity) / time taken

Acceleration An object travels in a straight line. The direction of motion does not change. Any change in the velocity is due to the change in speed Hence acceleration is also: Acceleration= change in speed time taken

Acceleration Example When the speed of a car changes from 5 m/s to 20 m/s in 5.0 seconds Acceleration= change in speed / time taken =(20m/s-5m/s) 5.0 seconds = 3.0m/s2

Acceleration at constant speed An object moving in a circle at constant speed is always accelerating (changing direction).

Solving Acceleration Problems using Acceleration Triangle Dv t

Acceleration Questions A dragster going at 15 m/s increases its velocity to 25 m/s in 4 seconds. What is its acceleration? The driver of a car steps on the brakes, and the velocity drops from 20 m/s to 10 m/s in a time of 2 seconds. Find his acceleration. Find the acceleration of a car that travels at a constant velocity of 45 Km/hr for 10 s.

Deceleration When the velocity decreases, the acceleration is negative and the accelerations is known as deceleration or retardation

Deceleration Example A car traveling at 20m/s takes 10 seconds to stop after the brakes are applied. What is its retardation? Solution Acceleration= final velocity -- initial velocity time taken = 0m/s- 20m/s 10 seconds = -2.0m/s Retardation=2.0 m/s2

Free fall, an example of acceleration Free fall is when an object is falling being affected only by gravity. That means NO air resistance.

Free Fall – All objects fall at the same rate If you drop a coin and a feather at the same time you will notice that the coin reaches the ground way before the feather. However, if you were to take the air out of the container you would find that the coin and feather fall together and hit the bottom at the same time!

Acceleration due to gravity, g Newton told us that every object with mass attracts every other object with mass and the size of the attraction depends on the mass of each object and the distance between the objects We don’t feel the attraction of most objects because their mass is small relative to the Earth which has a huge mass. The Earth pulls so that objects experience an acceleration of about 10 m/s2. This acceleration is given a special letter, g. g = 10 m/s2 This number is important, remember it! So during each second an object is in free fall, its velocity increases by 10 m/s. If the object experiences air resistance its velocity won’t increase as fast because air resistance will slow it down.

Challenge Question Suppose someone throws a ball straight upward with a speed of 30 m/s and at the same time throws one straight down with a speed of 30 m/s. Which ball will be traveling faster when it hits the ground, the one thrown straight upward or the one thrown straight down? Assume there is no air resistance.

Time and velocity for an object in free fall v = gt g v t

Time and Distance for an object in free fall d = ½ gt2

Free Fall Questions – How Fast? 1) When a ball is thrown straight down, by how much does speed increase each second on Earth? 2) When a ball is thrown straight up, by how much does speed decrease each second? 3) In free fall, do a feather and a ball fall side by side? Explain. 4) An apple falls freely from rest for 8 s on Earth, find its speed at 8 s. 5) Suppose a rock is dropped on a planet where the acceleration due to gravity it 5 m/s2, by how much would the speed change each second? 6) If a rocket on the planet in #5 falls from rest for 3 s, what is its speed at the end of the 3 s interval? 7) Challenge: Find g on a planet where a rock has a velocity of 120 m/s after 6s of free fall.

Free Fall Questions – How Far? For a freely falling rock does the distance fallen each second stay the same, increase with time, or decrease with time? A ball is dropped from rest and freely falls for 6 s. How many meters has it fallen in 6 s? A ball is thrown straight upward and travels 5 m until it reaches the top of its path. How far will it fall before it reaches its initial position? How long will it take to fall that distance? How long will the ball be in the air? 4) A ball is thrown straight up and returns to Earth 6 s later. Find its speed at the top of its path. Find its acceleration at the top its path. How long does it take to reach the top of its path? How fast is it traveling when it returns to Earth? Challenge: What is its maximum height?

Additional Free Fall Review If one had only a stopwatch, could one determine the initial speed of a ball launched vertically upward from the earth’s surface? Explain. With only a stopwatch, could one determine how high the ball travels before it stops? Explain.

Motion Graphs – Position vs. Time constant, rightward (+) velocity of +10 m/s a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Motion Graphs – Velocity vs. Time constant, rightward (+) velocity of +10 m/s a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Motion Graph Questions 1) What do you think might be happening in this graph? 2) What do you think position and velocity graphs of free fall motion might look like? Try to sketch them.