Chapter 2 Linear Motion Mechanics The cheetah is the fastest land animal and can achieve speeds of 100 km/hr. |
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Motion is relative. Everything moves; some things move more perceptibly. The study of motion of objects and the related concepts of force and energy is mechanics. Mechanics is divided into kinematics and dynamics. Objects that move without rotating are undergoing translational motion. Motion is relative. We say that everything is in relative motion, meaning we use a reference object or position to judge the motion. Our reference will be the surface of the Earth. Once a reference point is defined, a frame of reference can be established. Motion is relative. The position of an object(d) is the separation between that object and the reference point. Positive positions are to the right of the reference point and negative positions are to the left of the reference point. A quantity like position that requires both a magnitude and a direction is a vector quantity. Motion is relative. Distance needs no frame of reference. A quantity like distance having only magnitude is a scalar quantity. Motion is relative. The change in position of an object is called its displacement(Dd). As the change in position is seen, time changes also so that a time
interval(Dt) is found. The ratio Dd/Dt is called average speed, unless a direction is specified. Then it becomes average velocity. Speed is a rate of motion. If the average velocity of an object is the same for all time intervals, then the object moves at constant velocity or uniform velocity. There must be constant speed and constant direction. Motion is relative. If either the speed or the direction change, the velocity changes. Constant speed and constant velocity are not the same. Motion is relative. It is possible to graph how position depends on clock reading, or time. This is called a position-time graph. Sketch the graph that the data will generate.
Motion is relative. Instantaneous velocity
can be found by a series of operations where successive average velocities are found until the time interval is negligible. Then the tangent to the curve is drawn. The slope is the instantaneous velocity. We get this value only by using a graph. Taking the slope of a line is the same as taking the first derivative. v = lim Dx t--->0
Dt Instantaneous acceleration is defined in a similar way. Motion is relative. If we change the speed or the direction of motion or both, we change the velocity. If we consider how fast the change occurs, then we consider acceleration. a = Dv/Dt The unit is m/s/s. Acceleration applies to decreases as well as increases in speed. A decrease in acceleration is known as deceleration or negative acceleration. Motion is relative. The distance an object moves during an acceleration is dependent upon the time over which the motion takes place. The longer the time, the further the object moves. We found that the distance is proportional to the square of the time. s = ½ a t2 for an object starting from rest. Motion is relative. There is also a velocity-time graph. What will such a graph look like if velocity is constant? What will such a graph look like if velocity changes? What will the value for the area under the line on a velocity-time graph represent? Free Fall When an object is falling so that gravity is the only force affecting it, it is said to be in free fall. During each successive time period, the object falls faster due to the force exerted on it. It accelerates at 9.8 m/s/s. If an object is dropped off a cliff, how fast will it be going after one second has elapsed? How far does an object in free fall go? If an object falls for 1s, does it fall 10 m because it is falling at 10 m/s/s? Why? Suppose the object has some initial velocity. How does that affect the distance and the speed? Suppose an object has initial velocity other than zero…… Then the object travels for time t at that speed as well as for time t during the acceleration. Both activities must be taken into account. x = x0 + vit + ½ at2 when vi does not equal zero and x0 does not equal zero. Another useful relationship is vf = vi + at. One more is vf2 = vi 2 + 2ad. |
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