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In this chapter we study kinematics of motion in one dimension—motion along a straight line. Runners, drag racers, and skiers are just a few examples of motion in one dimension.
Chapter Goal: To learn how to solve problems about motion in a straight line.
• Uniform Motion• Instantaneous Velocity• Finding Position from Velocity• Motion with Constant Acceleration• Free Fall• Motion on an Inclined Plane• Instantaneous Acceleration
Kinematics in One DimensionKinematics in One Dimension
The slope at a point on a position-versus-time graph of an object is
A. the object’s speed at that point.B. the object’s average velocity at that point.C. the object’s instantaneous velocity at that point.D. the object’s acceleration at that point.E. the distance traveled by the object to that point.
The slope at a point on a position-versus-time graph of an object is
A. the object’s speed at that point.B. the object’s average velocity at that point.C. the object’s instantaneous velocity at that point.D. the object’s acceleration at that point.E. the distance traveled by the object to that point.
Straight-line motion in which equal displacements occur during any successive equal-time intervals is called uniform motion. For one-dimensional motion, average velocity is given by
Instantaneous VelocityAverage velocity becomes a better and better approximation to the instantaneous velocity as the time interval over which the average is taken gets smaller and smaller.
As Δt continues to get smaller, the average velocity vavg = Δs/Δt reaches a constant or limiting value. That is, the instantaneous velocity at time t is the average velocity during a time interval Δt centered on t, as Δt approaches zero.