Dr. Jie Zou PHY 1151G Department of Physics1 Chapter 2 One-Dimensional Kinematics (Cont.)

Dr. Jie Zou PHY 1151G Department of Physics2 Outline Acceleration Average acceleration Instantaneous acceleration Kinematics equation for one- dimensional motion under constant acceleration Free Fall

Dr. Jie Zou PHY 1151G Department of Physics3 Acceleration Average acceleration: the rate of change of velocity. a av =  v/  t = (v f – v i )/(t f – t i ). SI units: meter per second squared, (m/s 2 ). Instantaneous acceleration: acceleration at any instant of time. When acceleration is constant, the instantaneous and average accelerations are the same. Constant acceleration: Both the magnitude and direction do not change with time.

Dr. Jie Zou PHY 1151G Department of Physics4 Example: Average Acceleration The winner of this race was traveling at a speed of mi/h at the end of the quarter-mile course. The winning time was just s, what was the average acceleration during the race? (Answer: ~ 3g)

Dr. Jie Zou PHY 1151G Department of Physics5 More about the Directions of Velocity and Acceleration When the velocity and acceleration of an object have the same signs, the velocity and acceleration point in the same direction and the object speeds up. When the velocity and acceleration of an object have opposite signs, the velocity and acceleration point in opposite directions and the object slows down.

Dr. Jie Zou PHY 1151G Department of Physics6 (a)And (d): Car speeds up (b) And (c): Car slows down

Dr. Jie Zou PHY 1151G Department of Physics7 Kinematics Equation for 1D Motion under Constant Acceleration v av = (v i + v f )/2. Table 2-4

Dr. Jie Zou PHY 1151G Department of Physics8 Example-Full Speed Ahead A boat leaves at an initial speed of 1.50 m/s. It speeds up with an acceleration at 2.40 m/s 2. (a) How fast is the boat moving after accelerating for 5.00 s? (b) How far has the boat traveled in this time? (Answer: (a) 13.5 m/s (b) 37.5 m)

Dr. Jie Zou PHY 1151G Department of Physics9 Free Falling Objects A freely falling object is any object moving freely under the influence of gravity alone. In real situations, when air resistance can be neglected, the motion can be approximated as a free fall. Free fall Dropped (released) from rest Thrown downward Thrown upward

Dr. Jie Zou PHY 1151G Department of Physics10 Acceleration of Freely Falling Object Direction of the free fall acceleration: The acceleration of an object in free fall is directed downward. Magnitude of free fall acceleration, g g decreases with increasing altitude and g varies with latitude 9.80 m/s 2 is the average at the Earth’s surface Assuming the constant value of g=9.80 m/s 2 near the Earth surface, free fall is a 1D motion with constant acceleration Both the direction and magnitude do not change.

Dr. Jie Zou PHY 1151G Department of Physics11 Example: Free Fall 1. A person steps off the end of a 3.00-m-high diving board and drops to the water below. (a) How long does it take for the person to reach the water? (Answer: s) (b) What is the person’s speed on entering the water? (Answer: 7.67 m/s)

Dr. Jie Zou PHY 1151G Department of Physics12 Example: Free Fall 2. A volcano shoots out blobs of molten lava, called lava bombs, from its summit. A geologist observing the eruption uses a stopwatch to time the flight of a particular lava bomb that is projected straight upward. If the time for it to rise and fall back to its launch height is 4.75 s, and its acceleration is 9.81 m/s 2 downward, what is its initial speed? (Answer: 23.3 m/s) Real-World Physics!

Dr. Jie Zou PHY 1151G Department of Physics13 Example: Free Fall 3. A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 35.0 m/s 2. The acceleration period lasts for time 4.00 s until the fuel is exhausted. After that, the rocket is in free fall. Find the maximum height reached by the rocket (ignore air resistance). For answer, see class discussion.

Dr. Jie Zou PHY 1151G Department of Physics14 Homework See online homework assignment at Hand-written homework assignment: Chapter 2, Page 51, Problems: #48.