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Motion

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**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.

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**Position, Velocity, and Acceleration**

Position 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?

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**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.

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Velocity The 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.

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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.

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

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Velocity

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**Average and instantaneous velocity**

Average 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.

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Relative velocity Relative 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.

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**Using relative velocity**

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? Looking for: …the time in seconds. Given: … velocity of the people mover (1 m/s), the relative velocity of the walker (2 m/s), and the displacement (150 m). Relationship: Use this version of the velocity equation: t = Δx ÷ v Solution: t = 150 m ÷ (1 m/s + 2 m/s) = 150 m ÷ 3 m/s = 50 s

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Acceleration Acceleration is the rate at which velocity changes.

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Acceleration Acceleration 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.

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**Calculating acceleration**

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**Calculating acceleration**

A sailboat moves at 1 m/s. Wind increases its velocity to 4 m/s in 3 seconds. Calculate the acceleration. Looking for: .. the acceleration in m/s/s. Given: … the initial velocity (vi=1 m/s), final velocity (vf=4 m/s), and time (t=3 s) Relationship: Use: a = (vf – vi) ÷ t Solution: a = 4 m/s – 1 m/s = 3 m/s = 1 m/s 3 s 3 s

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Units of acceleration An acceleration in “meters per second per second (m/s/s) is often written m/s2 or meters per second squared.

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**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: = 39.2 m/s2 ,down

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**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.

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