Physics of Motion Displacement speed velocity acceleration and

Physics of Motion: Displacement, speed, velocity, acceleration and momentum

Displacement-time graphs • Y axis is displacement/distance (position) • X axis is time • Slope of a line at any point is the speed (velocity). • Slope = (y 2 – y 1)/(x 2 – x 1) • Positive slope of straight line indicates constant, positive speed • Negative slope indicates movement in opposite direction • Slope of zero (flat line) indicates object at rest • An increasing slope (curve upward) indicates positive acceleration (speeding up) • A decreasing slope indicates negative acceleration (slowing down)

Distance-time graph summary

Velocity-time graphs • Y axis is speed or velocity • X axis is time • Y value of zero means object is at rest. • Slope of a line at any point is the acceleration. • Positive slope of straight line indicates constant, positive acceleration • Negative slope indicates negative acceleration (slowing down) • Slope of zero (flat line) no acceleration, so constant velocity

Speed-time graph summary

Unit 1 c: Projectile motion!

Why is it worse to fall from greater heights (without a parachute)?

Acceleration due to gravity • On earth, in a vacuum, all objects fall with the same acceleration due to gravity: 9. 81 m/s 2 downward • Two objects of different weight (e. g. , feather and bowling ball) dropped from the same height will land at the same time

How long does it take to hit the ground? •

Let’s test it! Trial Time 1 Time 2 Time 3 Averag e time

Movement in two dimensions • Vectors (in two dimensions) can be broken down into vector components of each dimension. • Each component vector (for say, velocity) behaves and can be analyzed independently. • Plain English: the vertical velocity is not influenced by the horizontal velocity, and vice versa. of y t ci ball o l Ve non can Vx (horizontal velocity) Vy (vertical velocity)

Horizontally launched projectiles • The horizontal velocity should not change (ignoring air resistance) • The vertical velocity changes due to gravitational acceleration • A ball rolling off of a table should hit the floor at the same time as ball that was dropped from the same height simultaneously.

How to solve a horizontally launched projectile problem •

Practice • A ball rolls off of a 1. 00 meter-high table at a velocity of 1. 5 m/s. How far away from the table will it land? • Step 1: solve for time to hit ground using first equation • Step 2: solve for horizontal distance traveled using second equation

What about projectiles launched at an angle? ? ? • We need to break down a vector into its horizontal and vertical components…

To break a vector down into its dimensional components… • Draw a horizontal vector pointing in the same direction of the original vector • Draw a vertical vector pointing in the same direction • Make a right triangle. The original vector is the hypotenuse

How to calculate the magnitude of the component vectors • V m/ 0 =1 s 0° θ=3 Vx = 10 m/s * cos (30°) Vy = 10 m/s * sin (30°)