قسم الفيزياء - فيزياء عامة 1 - كلية التربية بالجبيل - جامعة الدمام د. غادة عميرة Motion in One Dimension

A particle’s position is the location of the particle with respect to a chosen reference point Position, Velocity, and Speed

position–time graph

displacement and distance The displacement of a particle is defined as its change in position in some time interval. vector quantity Distance is the length of a path followed by a particle. scalar quantity

Example 1: On this basketball court, The distance that the players run over the duration of the game is nonzero. The displacement of the players over the duration of the game is approximately zero because they keep returning to the same point over and over again.

speed and velocity The average velocity of a particle is defined as: The average speed of a particle, a scalar quantity, is defined as: average speed is always positive

For example, suppose it takes you 45.0 s to travel 100 m down a long straight hallway toward your departure gate at an airport. then, you return back 25.0 m along the same hallway, taking 10.0 s to make the return trip.

Keep in Mind That: The magnitude of the average velocity is not the average speed. For example, The magnitude of the average velocity for the marathon runner is zero, but the average speed is clearly not zero.

Quick Quiz 2.1 Under which of the following conditions is the magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval? (a) A particle moves in the +x direction without reversing. (b) A particle moves in the -x direction without reversing. (c) A particle moves in the +x direction and then reverses the direction of its motion. (d) There are no conditions for which this is true.

Instantaneous Velocity and Speed The instantaneous velocity: The instantaneous speed of a particle is defined as the magnitude of its instantaneous velocity.

Keep in Mind: -average velocity is not the average speed. But The magnitude of the instantaneous velocity is the instantaneous speed. - In an infinitesimal time interval, the magnitude of the displacement is equal to the distance traveled by the particle.

Example 2 if one particle has an instantaneous velocity of +25 m/s along a given line and another particle has an instantaneous velocity of -25 m/s along the same line, both have a speed of 25 m/s.

-average velocity is the slope slopes of the lines joining the points on the graph. - instantaneous velocity is the slope of the line tangent to the x-versus-t curve average velocity Instantaneous velocity

Example 3: Average and Instantaneous Velocity A particle moves along the x axis. Its position varies with time according to the expression where x is in meters and t is in seconds..

(A) Determine the displacement of the particle in the time intervals t = 0 to t = 1 s and t = 1 s to t = 3 s. -the displacement between t = 0 and t = 1 s is: -the displacement during the second time interval (t = 1 s to t = 3 s),

(B) Calculate the average velocity during these two time intervals. Solution: - In the first time interval -In the second time interval

(C) Find the instantaneous velocity of the particle at t = 2.5 s. Solution:

Acceleration The average acceleration of the particle is defined as: The SI unit of acceleration is meters per second squared (m/s 2 )

the instantaneous acceleration the term acceleration mean instantaneous acceleration.

When the object’s velocity and acceleration are in the same direction, the object is speeding up. On the other hand, when the object’s velocity and acceleration are in opposite directions, the object is slowing down.

Deceleration The word deceleration has the common popular connotation of slowing down

the velocity–time graph The instantaneous acceleration can be obtained from the velocity–time graph. At each instant, the acceleration equals the slope of the line tangent to the v x versus t.

Max a Max slope a=0 Slope=0 Slope=-ve a=-ve

A particle moving along the x axis with constant acceleration

Example 4:

Example 5: Average and Instantaneous Acceleration The velocity of a particle moving along the x axis varies in time according to the expression: where t is in seconds. (A) Find the average acceleration in the time interval t = 0 to t = 2.0 s. Solution

(B) Determine the acceleration at t =2.0 s.

constant positive velocity zero acceleration

Quick Quiz 2.4: Which of the following is true? (a) If a car is traveling eastward, its acceleration is eastward. (b) If a car is slowing down, its acceleration must be negative. (c) A particle with constant acceleration can never stop and stay stopped.

Displacement = area under the v x -t graph

Example 6: The displacement of the particle during the time interval t f - t i is equal to the area of the shaded rectangle.

Example 7: the displacement of the particle during the time interval t = 0 to t = t A is equal to the area of the shaded triangle

One-Dimensional Motion with Constant Acceleration The equations of kinematics:

Quick Quiz 2.5 : In Figure, match each v x -t graph on the left with the a x -t graph on the right that best describes the motion.

Example 8: Carrier Landing

A freely falling object is any object moving freely under the influence of gravity alone, regardless of its initial motion. Objects thrown upward or downward and those released from rest are all falling freely once they are released. Any freely falling object experiences an acceleration directed downward, regardless of its initial motion. Freely Falling Objects

Quick Quiz 2.6 A ball is thrown upward. While the ball is in free fall, does acceleration (a) increase (b) decrease (c) increase and then decrease (d) decrease and then increase (e) remain constant?

Quick Quiz 2.7 After a ball is thrown upward and is in the air, its speed (a) increases (b) decreases (c) increases and then decreases (d) decreases and then increases (e) remains the same.

One-Dimensional Motion with gravity Acceleration The equations of kinematics: g = 9.8m/s2 Up ward g =- 9.8m/s2 dawn ward g = +9.8m/s2

Qestion:2

Question: 3

Q :4

Q: 5

Q:7

Q: 8

P: 3

P:4

P :6

P :15

P: 20

P: 47

Problems:5, 14,16, 25, 33, 46 Exercises: