Kinematics in One Dimension

Kinematics in One Dimension

Distance and Displacement

Distance and Displacement Starting from origin, O a person walks 90-m east, then turns around and walks 40-m west.

Distance and Displacement Starting from origin, O a person walks 90-m east, then turns around and walks 40-m west.

Q: What is the total walked distance?

Distance and Displacement Starting from origin, O a person walks 90-m east, then turns around and walks 40-m west.

Q: What is the total walked distance? A: 130-m

Distance and Displacement Starting from origin, O a person walks 90-m east, then turns around and walks 40-m west.

Q: What is the total walked distance? A: 130-m

Q: What is the displacement?

Distance and Displacement Starting from origin, O a person walks 90-m east, then turns around and walks 40-m west.

Q: What is the total walked distance? A: 130-m

Q: What is the displacement? A: 50-m, due east.

Displacement

The displacement d is a vector that points from the initial position di to the final position df.

d = df - di

SI Unit of Displacement: meter (m)

2.2 Speed and Velocity

•Average Speed

•Average Velocity

•Instantaneous Velocity

•Instantaneous Speed

Average Speed

Units for speed: m/s, MPH, kmPH.

Average Velocity

Units for velocity: m/s, MPH, kmPH.

Acceleration

Acceleration

Units: m/s2, cm/s2

Deceleration

DecelerationAn object speeds up when the acceleration and velocity vectors point in the same direction.

DecelerationAn object speeds up when the acceleration and velocity vectors point in the same direction.

Whenever the acceleration and velocity vectors have opposite directions, the object slows down and is said to be “decelerating.”

DecelerationAn object speeds up when the acceleration and velocity vectors point in the same direction.

Whenever the acceleration and velocity vectors have opposite directions, the object slows down and is said to be “decelerating.”

Example 4: A drag racer crosses the finish line, and the driver deploys a parachute and applies the brakes to slow down. The driver begins slowing down when t0 = 9.0 s and the car's velocity is v0 = +28 m/s. When t = 12.0 s, the velocity has been reduced to v = +13 m/s. What is the average acceleration of the dragster?

Kinematics Equations

2.6 Freely Falling Bodies

2.6 Freely Falling Bodies

In the absence of air resistance, it is found that all bodies at the same location above the earth fall vertically with the same acceleration.

2.6 Freely Falling Bodies

In the absence of air resistance, it is found that all bodies at the same location above the earth fall vertically with the same acceleration.

Furthermore, if the distance of the fall is small compared to the radius of the earth, the acceleration remains essentially constant throughout the fall.

2.6 Freely Falling Bodies

In the absence of air resistance, it is found that all bodies at the same location above the earth fall vertically with the same acceleration.

Furthermore, if the distance of the fall is small compared to the radius of the earth, the acceleration remains essentially constant throughout the fall.

This idealized motion, in which air resistance is neglected and the acceleration is nearly constant, is known as free-fall.

2.6 Freely Falling Bodies

In the absence of air resistance, it is found that all bodies at the same location above the earth fall vertically with the same acceleration.

Furthermore, if the distance of the fall is small compared to the radius of the earth, the acceleration remains essentially constant throughout the fall.

This idealized motion, in which air resistance is neglected and the acceleration is nearly constant, is known as free-fall.

Since the acceleration is constant in free-fall, the equations of kinematics can be used.

Acceleration Due to GravityThe acceleration of a freely falling body is called the acceleration due to gravity, g.

The acceleration due to gravity is directed downward, toward the center of the earth.

Near the earth's surface, g = 9.80 m/s2, down.

Heavy and light objects fall at the same rate

A Falling StoneA stone is dropped from rest from the top of a tall building, as the figure indicates.

After 3.00 s of free-fall, a. what is the velocity v of the stone?

b. what is the displacement y of the stone?

Coin TossA football game customarily begins with a coin toss to determine who kicks off. The referee tosses the coin up with an initial speed of 6.00 m/s. In the absence of air resistance, how high does the coin go above its point of release?

What is the velocity and acceleration at the maximum height?

2.7 Graphical Analysis of Motion

First we will graphically look at a motion where a person walks at a constant velocity along a straight-line path.

2.7 Graphical Analysis of Motion

First we will graphically look at a motion where a person walks at a constant velocity along a straight-line path.

Can you plot the position, x (m) versus time, t (s) graph?

Position VS. Time graph

What is the slope of the position VS. time graph?

Position VS. Time graph

What is the slope of the position VS. time graph?

Velocitytd

RunRiseSlope

EXAMPLE 16 A Bicycle TripA bicyclist maintains a constant velocity on the outgoing leg of a journey, zero velocity while stopped for lunch, and another constant velocity on the way back.

Velocity versus Time graph

A car is moving along a straight-line path starting from rest at a constant acceleration. Once the car reaches a velocity of 45 MPH, that velocity is maintained for a while. Finally the brakes are applied with a constant deceleration and the car comes to rest.

Velocity versus Time graph

A car is moving along a straight-line path starting from rest at a constant acceleration. Once the car reaches a velocity of 45 MPH, that velocity is maintained for a while. Finally the brakes are applied with a constant deceleration and the car comes to rest.

Can you plot Velocity VS. Time for the car?

Velocity VS. Time

The slope of the velocity versus time graph is the acceleration.

onAcceleratitV

RunRiseSlope

The area under the velocity versus time graph is the displacement.

Problem

A snowmobile moves according to the velocity-time graph shown in the drawing.

a. What is the snowmobile’s average acceleration during each of the segments A, B, and C?

b. How far it travels during each of the segments A, B, and C?