motion. 2.1 investigation: position, speed, and velocity key question: how are position, speed, and...

Motion

2.1 Investigation: Position, Speed, and Velocity

Key Question:

How are position, speed, and velocity related?

Objectives:

Measure positive and negative positions.

Measure positive and negative velocity.

Compare speed and velocity.

Position, Velocity, and AccelerationPosition is a variable.

Position and distance are similar but not the same. Both use units of length.

Position is given relative to an origin.

If a car moves 20 cm, what is it’s new

position?

Position and displacement A change in position is called displacement.

A displacement of –20 cm means the car leaves the 50-cm mark and moves toward the origin.

A displacement of 20 cm means the car moves away from the origin.

VelocityThe velocity of an object (v) tells

you both its speed and its direction of motion.

Velocity can be positive or negative, so it includes information about the moving object’s direction.

Constant velocity means that both the speed and the direction an object is traveling remains constant.

Positive velocity

The sign for velocity is based on the calculation of a change in position.

The change in position is the final position minus the initial position.

Negative velocity

Negative velocity means the position is decreasing relative to the starting point.

Velocity

Average and instantaneous velocityAverage velocity is the total displacement divided

by the total time taken.

Instantaneous velocity describes the velocity of an object at one specific moment in time or at one specific point in its path.

Relative velocityRelative velocity

describes the velocity of an object with respect to a frame of reference.

If you are sitting in a chair, you are not moving relative to Earth, but you are moving at about 67,000 mph relative to the Sun.

A people mover has a velocity of 1 m/s and is 150 m long. If a man walks 2 m/s relative to the people mover, how long will it take him to reach the opposite end if he walks in the direction that the people mover travels?

Using relative velocity

1. Looking for: …the time in seconds.

2. Given: … velocity of the people mover (1 m/s), the relative velocity of the walker (2 m/s), and the displacement (150 m).

3. Relationship: Use this version of the velocity equation:

t = Δx ÷ v

4. Solution: t = 150 m ÷ (1 m/s + 2 m/s)

= 150 m ÷ 3 m/s = 50 s

Acceleration

Acceleration is the rate at which velocity changes.

AccelerationAcceleration and velocity are completely different

ways to describe an object’s motion.

An object can be accelerating when its velocity is zero.

Like velocity, acceleration can be positive or negative.

An object will have a positive acceleration when it is speeding up in the positive direction, and when it is slowing down in a negative direction.

Calculating acceleration

A sailboat moves at 1 m/s. Wind increases its velocity to 4 m/s in 3 seconds. Calculate the acceleration.

Calculating acceleration

1. Looking for: .. the acceleration in m/s/s.

2. Given: … the initial velocity (vi=1 m/s), final velocity (vf=4 m/s), and time (t=3 s)

3. Relationship: Use: a = (vf – vi) ÷ t

4. Solution: a = 4 m/s – 1 m/s = 3 m/s = 1 m/s

3 s 3 s

Units of accelerationAn acceleration in “meters per second per second

(m/s/s) is often written m/s2 or meters per second squared.

Constant acceleration

The velocity vs. time graph shown is for a ball in free fall.

Since the ball is accelerated by gravity, it’s velocity increases by the same amount: 9.8 m/s2.

What is the velocity of the ball after 4 seconds?Ans: 29.4 + 9.8 = 39.2 m/s2 ,down

Constant acceleration

Don’t confuse constant velocity with constant acceleration.

Constant velocity means an object’s position changes by the same amount each second.

Constant acceleration means an object’s velocity changes by the same amount each second.