Reference: Beginning Physics I
CHAPTER 2: MOTION IN A STRAIGHT LINE
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KEY WORD LIST
Kinematics, Coordinate System, One-Dimensional, Particle, Displacement, Time, Velocity, Distance, Speed, Acceleration, Case of Constant Acceleration, Freely Falling Bodies
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GLOSSARY
For details on the following concepts, please consult CHAPTER 2.
KINEMATICS
Kinematics is the study of physical quantities that describe the motion of an object.
COORDINATE SYSTEM
Origin: “order together.” A coordinate system is a fixed system of directions and angles from an ‘origin point’ that uses numbers to define the position of a point, line, or the like.
ONE-DIMENSIONAL
One-dimensional means, in a straight line; in the same direction; along the x-axis.
PARTICLE
In mechanics, a particle is an infinitesimally small object located at a definite point in a coordinate system. The particle is the representation of the mathematical ‘center of mass’ of an object. If there is no center of mass, as in the case of a “light particle” then the laws of mechanics do not apply.
DISPLACEMENT
Displacement is the measure of the position of the object in a coordinate system. Absolute displacement specifies a particle’s location as measured from the origin. It has both a magnitude and a sign. Its magnitude is the straight-line distance from the origin to the location of a particle. Its sign is positive if the particle is on the positive side of the axis, and negative if it is on the negative side. Relative displacement is the location of the particle as measured from an arbitrary point. Like absolute displacement, relative displacement can be either positive or negative. If right is chosen as the positive direction, then the relative displacement is negative when the position of the particle is to the left of the position from which it is measured.
TIME
Time is a measure of when the object is at a certain position in a coordinate system. Time elapsed is always positive.
VELOCITY
Velocity is the time rate of change of displacement.
The average velocity is defined as,
Since the time difference in the denominator is always positive, the sign of average velocity is the sign of the relative displacement, and thus it indicates whether the particle has moved to the right (plus) or to the left (minus).
Instantaneous velocity is the velocity of the particle at a given instant of time. It is determined by the slope of the tangent line to the x-t curve at any time. The instantaneous velocity at time t1 is given by
DISTANCE
Distance is the absolute value of the relative displacement. Therefore, the distance traveled is always positive.
SPEED
Average speed is defined as the total distance traveled in a given time divided by that time interval. Since distance traveled is always positive, the average speed is always positive. Its units are the same as those of velocity. Average speed is either equal to or greater than the average velocity. Instantaneous speed is always the same as instantaneous velocity.
ACCELERATION
Acceleration is the time rate of change of velocity.
The average acceleration is defined as,
Like velocity, acceleration can be positive, negative or zero.
Instantaneous acceleration is the acceleration of the particle at a given instant of time. It is determined by the slope of the tangent line to the v-t curve at any time. The instantaneous acceleration at time t1 is given by
CASE OF CONSTANT ACCELERATION
For a particle starting at origin, x = 0, t = 0, and v = v0. Also, x = displacement from origin, and t = time elapsed.
FREELY FALLING BODIES
A body falling freely under gravitation has
- Constant downward acceleration (g) of 9.81 m/s2, or 32.2 ft/ s2
- Negligible air resistance.
Since the acceleration of gravity is in the negative y direction, we have a = -g. Also, v0= 0 and y0= 0. Therefore,
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