Acceleration Nonuniform Motion Diagrams An object with uniform

Acceleration

Nonuniform Motion Diagrams • An object with uniform motion moves along a straight line with an unchanging velocity, but few objects move this way. • Nonuniform motion is more common than uniform motion. • In nonuniform motion, velocity is changing.

Nonuniform Motion Diagrams • The distance the jogger moves in each time interval indicates the type of motion. Motion Diagram

Nonuniform Motion Diagrams • The rate at which an object’s velocity changes is called the acceleration (a) of the object. • Acceleration is measured in m/s 2. • Like displacement and velocity, acceleration is a vector. • When the velocity of an object changes at a constant rate, it has a constant acceleration. • Acceleration can occur when speed is constant, but the direction of the object is changing.

Nonuniform Motion Diagrams • The change in length of the velocity vectors on these motion diagrams indicates whether the jogger is speeding up or slowing down.

Nonuniform Motion Diagrams • You can determine the length and direction of an acceleration vector by subtracting two consecutive velocity vectors and dividing by the time interval.

Direction of Acceleration • You need to know the direction of both the velocity and acceleration vectors in order to determine whether an object is speeding up or slowing down. • When the acceleration of an object is in the same direction as its velocity, the object’s speed increases , as shown on the first and third rows on the next slide. • When the acceleration of an object is in the opposite direction as its velocity, the object’s speed decreases , as shown on the second and fourth rows on the next slide.

Direction of Acceleration

Calculating Acceleration • Average acceleration is defined as the change in velocity divided by the time it takes to make that change. The equation for average acceleration is shown below.

Calculating Acceleration Use with Example Problem 1. Problem Use the v-t graph below to answer the following questions. a. What is the object’s average acceleration between 20. 0 s and 40. 0 s? b. What is the object’s instantaneous acceleration at 30. 0 s? Response A SKETCH AND ANALYZE THE PROBLEM • List the knowns and unknowns. • For part a, the velocity at the needed times can be found on the graph. KNOWN UNKNOWN v 20 = 4. 0 m/s ā=? v 40 = 0. 0 m/s Δt = 20. 0 s SOLVE FOR THE UNKNOWN • Use the definition of average acceleration. EVALUATE THE ANSWER • The units are correct: Acceleration is measured in m/s 2.

Calculating Acceleration Response B Use with Example Problem 1. SKETCH AND ANALYZE THE PROBLEM • List the knowns and unknowns. • For part b, draw a line tangent to the curve at the point t = 30. 0 s and find the slope of the line. Problem Use the v-t graph below to answer the following questions. a. What is the object’s average acceleration between 20. 0 s and 40. 0 s? ā = − 0. 20 m/s 2 b. What is the object’s instantaneous acceleration at 30. 0 s? KNOWN (x 1, y 1) = (25. 0 s, 4. 0 m/s) UNKNOWN a=? (x 2, y 2) = (40. 0 s, 2. 0 m/s) SOLVE FOR THE UNKNOWN • Calculate the slope of the tangent line to find the instantaneous acceleration. EVALUATE THE ANSWER • The units are correct: Acceleration is measured in m/s 2.

Calculating Acceleration Use with Example Problem 2. Problem On a test track, a professional driver preforms a 0 to 60 test. That is, she starts the car at rest and accelerates as quickly as possible to 60 miles per hour (28. 6 m/s). If the small sedan she is testing has a 0 to 60 time of 8. 5 seconds, what is the car’s average acceleration? KNOWN UNKNOWN vi = 0. 0 m/s ā=? vf = 28. 6 m/s Δt = 8. 5 s SOLVE FOR THE UNKNOWN • Use the definition of average acceleration. Response SKETCH AND ANALYZE THE PROBLEM • Sketch the situation. • List the knowns and unknowns. EVALUATE THE ANSWER • The units are correct: Acceleration is measured in m/s 2. • The sign agrees with the drawing. • A quick estimate reveals that the magnitude is reasonable: 30/9 = 3. 3.

Quiz 1. In a particle model diagram, how do you identify nonuniform motion? A The dots are unevenly spaced. C Look for signs of velocity changes. B The vectors are different lengths. D all of the above CORRECT

Quiz 2. If a car’s acceleration is in the same direction as its velocity, what happens to the car’s speed? A The speed of the car does not change. B The speed of the car increases. C The speed of the car decreases. D There is not enough information to determine the car’s speed. CORRECT

Quiz 3. Which line or lines on the graph represent positive acceleration if east is the positive direction? A A and E C B and D CORRECT B C D B, C, and D

Quiz 4. Using the graph, determine the average acceleration between 2 s and 4 s. A 2. 0 m/s 2 B 4. 0 m/s 2 C 6. 0 m/s 2 CORRECT D 8. 0 m/s 2

Quiz 5. You can determine which factor of an object in motion by determining the slope of a tangent line on the velocity-time graph at the point in which you are interested? A instantaneous acceleration CORRECT C velocity B average acceleration D speed