Motion under constant acceleration Mr. Weissbard

Physics Standards CA content standards: Physics 1c Students know how to apply the law F=ma to solve one-dimensional motion problems that involve constant forces (Newton's second law). NGSS:HS-PS2-1. Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. [Clarification Statement: Examples of data could include tables or graphs of position or velocity as a function of time for objects subject to a net unbalanced force, such as a falling object, an object rolling down a ramp, or a moving object being pulled by a constant force.] [Assessment Boundary: Assessment is limited to one-dimensional motion and to macroscopic objects moving at non-relativistic speeds.]

Learning Objective To understand the behavior of objects under constant acceleration and to predict velocity and position using graphs and formulas. Warm Up: {FM} Write the equation of motion (formula) for an object (particle) moving at constant velocity. Sketch.

Web Resources video: Apollo 11 Launch: <a target="_blank" href= "https://www.youtube.com/watch?v=F0Yd- GxJ_QM">https://www.youtube.com/watch?v=F0Yd -GxJ_QM</a> Questions: What did you observe? Why did the rocket's velocity increase? Why did they jettison the first stage rocket booster?

Average velocity Instantaneous velocity What is velocity? What does the word average mean? What does the word instantaneous mean?

Average and instantaneous velocity velocity v {m/s} velocity v {m/s} average value average value time t {s} time t {s}

How can we use velocity to calculate the distance an object travels? Suggest 2 ways to solve this problem assume velocity is changing in a linear fashion i.e. straight line hint: the distance travelled is the area under the curve d = vavg x t Does this formula apply to both graphs on the previous slide?

Find the distance travelled Find 2 different ways to solve this problem 2 v {m/s} 1 1 2 t {s}

Acceleration Acceleration is defined as the change in velocity for a given time Average acceleration is defined as the total change in velocity over a given period of time Instantaneous acceleration is how the velocity is changing at a particular moment

Average and instantaneous acceleration velocity v {m/s} velocity v {m/s} time t {s} time t {s} Think: average slope Think: instantaneous slope

A more complicated problem Find the distance travelled Find 2 different ways to solve this problem 4 3 v {m/s} 2 1 1 2 t {s}

Sample problems: A bicycle is moving at 2 m/s when it crosses the starting line. The rider accelerates steadily at a rate of 1 m/s every second for 5 seconds. How fast is he moving after 5 seconds? What was his average velocity form 0 to 5 seconds? How far did he travel in the 5 seconds after he crossed the staring line?

Wrap Up What have we learned today? the difference between average and instantaneous how to find distance travelled from a v vs t graph the definition of acceleration formulas to calculate distance travelled (assuming constant acceleration)