Speed, Velocity & Acceleration 9/27/10

Speed, Velocity & Acceleration9/27/10

Position vs Distance • Position is an objects location compared with where it started, including direction • Distance is a length without regard to direction • If you walk 7 km north of school this is your position. If you walk back to the school your position is zero even though you walked 14 km. (7km away plus 7 km back)

If there are turns, the position might be different from the distance traveled

The position vs time graph shows where an object is at different times Speed is the slope of the position vs time graph Position vs time graph

Instantaneous and Average Speed • Does your speed stay the same during a real trip? • Of course not! You stop at lights, speed up to pass • Average speed is how fast something moves over a certain distance • You travel 50 km in 2 hours average speed = 25 km/hr • Instantaneous speed is the speed of an object at a specific point in its journey

Avg speed = 50 km = 2 hr 25 km/hr Δd = df – di = 10km – 0km = 10km Δt tf – ti 0.5 hr – 0 hr 0.5 hr

Avg speed = 50 km = 2 hr 25 km/hr Δd = df – di = 15km – 10km = 5 km Δt tf – ti 1 hr – 0.5 hr 0.5 hr

Avg speed = 50 km = 2 hr 25 km/hr Δd = df – di = 30km – 15km = 15km Δt tf – ti 1.25 hr – 1 hr .25 hr

Speed vs. Velocity • Speed is a description of how fast an object moves • Velocity is how fast an object moves and the direction in which it moves; if either the speed or the direction (or both) of an object is changing, the velocity is changing. • There are 3 controls in a car that can change velocity. They are….?

Acceleration • Acceleration is the rate of the change of velocity • Rate of change means the ratio of the amount of change divided by how much time it took to change Acceleration = Change in velocity Change in time (Δt)

Key idea for acceleration? • Change – whenever we change our state of motion, we are accelerating • Acceleration applies to decreases (deceleration or negative acceleration) and increases in speed and any change in direction • When addressing only straight-line motion, acceleration can be the rate at which speed changes.

Units are cm/sec2

Types of Acceleration • There are three different types of acceleration: positive, negative, and zero acceleration • Positive acceleration means the object is speeding up • Negative acceleration means the object is slowing down • Zero acceleration means the object is keeping the same speed

Calculating Acceleration • Acceleration is the slope of the speed vs time graph

If a car speeds up, without changing direction, from 0 to 10 km/h in 1 second, our acceleration is change in speed10 km/h Acceleration = time interval = 1s = 10 km/h-s Two time entries in answer; first for unit of speed (km/h), second for time interval in which speed is changing (-s)

Practice problem #1 • A swimmer speeds up from 1.9 m/s to 2.6 m/s during the last 20 seconds of a workout. What is the swimmer’s acceleration during this time interval?

Practice problem #2 • 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. • Which undergoes greater acceleration? • What is the acceleration of each vehicle?

Practice problem #3 • Match each of the three distance vs time graph with the corresponding speed vs time graph.

Momentum

Momentum • Momentum is the mass of an object multiplied by its speed or velocity. • If you increase the mass or the speed of an object, you increase its momentum. • Units are kg m/s

Mass (kg) Velocity (m/s) Momentum (kgm/s)

If you throw a ball from your skateboard, you must apply a force to the ball. The 3rd law says the ball exerts a force an equal and opposite force on you. Your force makes the ball accelerate in one direction and the reaction makes you accelerate in the opposite direction. The motion of objects

If you throw the ball away very fast, you backward acceleration is higher than if you throw the ball away slowly. If you throw a heavier ball away fast, you backward acceleration is greater than if you throw a lighter ball. The backward acceleration is called recoil. What happens if you throw a heavier ball?

Law of Conservation of Momentum • The law of the conservation of momentum says that the total momentum of a system can not change. • That means that the momentum of the system prior an action must equal the momentum after the action.

Positive and negative signs are used to tell the direction of the motion. That means momentum can be positive (moving to the right) or negative (moving to the left) Before you throw the ball, your and the ball’s momentum is zero. In order for conservation of momentum to be true, after you throw the ball the total momentum must be zero. (1 kg)(-20 m/s) + (40kg)(0.5m/s) = 0

Homework 19 • Compare the momentums of a 65 kg dolphin swimming 11.3 m/s and a 6500 kg elephant walking 0.11 m/s.

Homework 23 • A girl is riding her bike at a speed of 6 m/sec. She then slows down to a speed of 2.5 m/sec. The combined mass of the girl and bicycle is 50 kilograms. • What is her initial momentum? • What is her final momentum? c. What is the change in momentum?

Speed, Velocity & Acceleration 9/27/10