What You Will Learn In This Chapter. Displacement Vector Distance Velocity Vectors Acceleration Vectors Motion with constant Acceleration

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1 Chapter 2

2 What You Will Learn In This Chapter Displacement Vector Distance Velocity Vectors Acceleration Vectors Motion with constant Acceleration

3 2.1 Introduction to kinematics Kinematics is the study of the motion of objects. These objects can be cars, baseballs, people, planets, or atoms. Motion in a straight line means motion of an object traveling in a straight line or in one dimension.

4 The object s position is its location with respect to a chosen reference point. Consider the point to be the origin of a coordinate system In the diagram, allow the road sign to be the reference point Position

5 Position-Time Graph

6 Displacement vector and distance Displacement can be positive or negative and is a vector quantity Distance is always positive and is a scalar quantity

7 Average Velocity The average velocity is a vector quantity and defined as rate at which the displacement occurs( change in displacement in time interval. The average velocity of a particle moving in one dimension can be positive or negative, depending on the sign of the displacement

8 Average Speed The average speed of a particle, a scalar quantity, is defined as the total distance traveled divided by the total time interval required to travel that distance: The average speed has no direction and thus it is always positive

9 Average velocity and Average Speed Knowledge of the average velocity or average speed of a particle does not provide information about the details of the trip. Example: Suppose it takes you 45.0s to travel 100m down a long straight hallway toward your departure gate at an airport. At the 100-m mark, you realize you missed the rest room, and you return back 25.0m along the same hallway, taking 10.0s to make the return trip. The magnitude of the average velocity for your trip is 75 m/55s=1.36m/s. The average speed for your trip is 125 m/55s=2.27 m/s. You may have traveled at various speeds during the walk. Neither average velocity nor average speed provides information about these details.

10 Example 2.1 Find the displacement, average velocity, and average speed of the car in the Figure between positions A and F x a = 30m at t=0 s x f =53m at t=50s.

11 Instantaneous Velocity The instantaneous velocity indicates what is happening at every point of time The instantaneous velocity can be positive, negative, or zero

12 Acceleration Vector The instantaneous acceleration : is the limit of the average acceleration as t approaches zero

13 Example 2.2 Find the instantaneous acceleration at Point A, B and C.

14 Example 2.3 During the time interval from 0.0 to 10.0 s, the position vector of a car on a road is given by: x(t) = 3t 2 + 5t What is the car s velocity as a function of time? 2- What is the car s average velocity during this interval? Solution: 1-2- and

15 Displacement & Velocity and Acceleration Note that: we often refer to the deceleration of an object as a decrease in the speed the object over time, which corresponds to acceleration in the opposite direction of the motion of the object. If the velocity and acceleration are in the same direction, the object moves faster. If the velocity and acceleration are in the opposite directions, the object moves slows down.

16 Class work 1 Which of these statement is true? 1. An object can have zero acceleration and be at rest. 2. An object can have nonzero acceleration and be at rest. 3. An object can have zero acceleration and be in motion. ***** chose the correct answer.***** 4- A car maintains a constant velocity of 100 km/hr for 10 seconds. During this interval it acceleration is a) zero. b) 10 m/s 2. c) 2.1 m/s 2. d) 1.5 m/s Which case of these has zero acceleration? An object a) at rest. b) moving at constant velocity. c) in mechanical equilibrium. d) all of these. Ans: 1- T, 2-F, 3- T 4- a, 5- d

17 One-Dimensional Motion with Constant Acceleration If the acceleration of a particle varies in time, its motion can be complex and difficult to analyze. However, a very common and simple type of one-dimensional motion is that in which the acceleration isconstant

18 Example 2.4 Accelerating from rest, a top fuel race car can reach mph (= m/s), a record at the end of a quarter mile (= m), assume constant acceleration. ( I ) What is the value of the race car s constant acceleration? Solution: from equation ( V ), Accelerating from rest. x 0 = 0, V x0 = 0

19 Example 2.4 ( I I ) How long does it take the race car to complete a quarter-mile run from a standing start? Solution: from equation (I I I ) s

20 Free fall The acceleration due to the gravitational force is constant. The acceleration due to gravity near the surface of the Earth has the value g = 9.81 m/s2. We call the vertical axis the y-axis and define the positive direction as up. Then the acceleration vector has only a nonzero y-component, which is given by

21 Free fall.cont This situation is a specific application of motion with constant acceleration. We use y instead of x to indicate that the displacement takes place in the y-direction. Then we obtain five kinematical equations.