Since velocity is a vector quantity involving speed and direction, acceleration occurs when the speed of an object changes, and/or the direction of the object changes.
The definition of acceleration can be expressed mathematically as,
The acceleration due to gravity is a constant rate of acceleration. It is negative because its direction is negative (it always acts down, or toward the center of the earth). The acceleration due to gravity is independent of the mass of the object. In a vacuum, all objects, regardless of mass, accelerate at the same rate. The magnitude of the acceleration due to gravity is dependent upon the distance of the object from the center of the earth. Galileo postulated that all objects would fall with the same constant acceleration in the absence of air or other resistance.
The velocity and acceleration of an object are not necessarily in the same direction. When a ball is thrown upward, its velocity is positive (upward), but its acceleration is downward (negative). At its highest point, a ball thrown upward has a velocity of zero. Its acceleration is still -9.8 m/s^{2}
In physics, the relationship between variables is examined graphically. If you wanted to experimentally determine the acceleration of an object, you would collect distance and time data. If for each time interval, the distance that the object travels is changing, the object is accelerating. From this data, you would determine the instantaneous velocity of the object at each instant of time. Since your velocity depends upon the elapsed time, velocity (dependent variable) is graphed on the y-axis and time (dependent variable) is graphed on the x-axis. The slope of the line gives the acceleration of the object.
On a velocity vs time graph, a line of constant slope indicates that the object has uniform (constant) acceleration. A horizontal line (a slope of zero) indicates that the object has zero acceleration and is moving at constant velocity. On a graph, if a line has positive slope, we say that the object has positive acceleration; if the line has negative slope, we say that the line has negative acceleration.
On a v vs t graph, you can mathematically write the equation for the motion of the object knowing the slope and the y-intercept. Remember, the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
The total displacement between any two times on a velicty vs time graph is equal to the area under the curve between the two times.
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