MOTION IN ONE DIMENSION CHAPTER TWO MOTION IN ONE DIMENSION

The Cheetah: A cat that is built for speed The Cheetah: A cat that is built for speed. Its strength and agility allow it to sustain a top speed of over 100 km/h. Such speeds can only be maintained for about ten seconds. Photo © Vol. 44 Photo Disk/Getty

Objectives: After completing this module, you should be able to: Define and apply concepts of average and instantaneous velocity and acceleration. Solve problems involving initial and final velocity, acceleration, displacement, and time. Demonstrate your understanding of directions and signs for velocity, displacement, and acceleration. Solve problems involving a free-falling body in a gravitational field.

Uniform Acceleration in One Dimension: Motion is along a straight line (horizontal, vertical or slanted). Changes in motion result from a CONSTANT force producing uniform acceleration. The cause of motion will be discussed later. Here we only treat the changes. The moving object is treated as though it were a point particle.

Distance and Displacement Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below: Distance s is a scalar quantity (no direction): A B s = 20 m Contains magnitude only and consists of a number and a unit. (20 m, 40 mi/h, 10 gal)

Distance and Displacement Displacement is the straight-line separation of two points in a specified direction. A vector quantity: Contains magnitude AND direction, a number, unit & angle. (12 m, 300; 8 km/h, N) A B D = 12 m, 20o q

Definition of Velocity Velocity is the displacement per unit of time. (A vector quantity.) A B s = 20 m Time t = 4 s D=12 m 20o v = 3 m/s at 200 N of E Direction required!

The Signs of Velocity - - + Velocity is positive (+) or negative (-) based on direction of motion. + - First choose + direction; then v is positive if motion is with that direction, and negative if it is against that direction. + - +

Definition of Acceleration An acceleration is the change in velocity per unit of time. (A vector quantity.) A change in velocity requires the application of a push or pull (force). The direction of accel- eration is same as direction of force. The acceleration is proportional to the magnitude of the force.

Acceleration and Force Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force.

The Signs of Acceleration Acceleration is positive (+) or negative (-) based on the direction of force. Choose + direction first. Then acceleration a will have the same sign as that of the force F —regardless of the direction of velocity. + F a (-) F a(+)

Average acceleration: Definitions Average velocity: Average acceleration:

Review of Symbols and Units Displacement (x, xo); meters (m) Velocity (v, vo); meters per second (m/s) Acceleration (a); meters per s2 (m/s2) Time (t); seconds (s) Review sign convention for each symbol

The Signs of Displacement Displacement is positive (+) or negative (-) based on LOCATION. 2 m -1 m -2 m The displacement is the y-coordinate. Whether motion is up or down, + or - is based on LOCATION.

The Signs of Velocity Velocity is positive (+) or negative (-) based on direction of motion. + + - First choose + direction; then velocity v is positive if motion is with that + direction, and negative if it is against that positive direction.

Acceleration Produced by Force Acceleration is (+) or (-) based on direction of force (NOT based on v). F a(-) a(+) A push or pull (force) is necessary to change velocity, thus the sign of a is same as sign of F. More will be said later on the relationship between F and a.