# Acceleration

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Acceleration of a body in motion is defined as the change in velocity in one second or rate of change of velocity. Mathematically, acceleration is equal to the change in velocity upon time taken. In SI system, unit of acceleration is ms-2 and in CGS system, its unit is cms-2. Depending on the rate of change of velocity, the motion of a body may be uniformly or non – uniformly accelerated.

The slope of the curve of velocity – time graph gives acceleration. The velocity – time graph of a uniformly accelerated body is a straight line. Magnitude of instantaneous acceleration of a body is given by the slope of the tangent to any point on the curve. Distance covered by a body in a certain time interval is equal to the area occupied below velocity – time graph, a curve inclined at an acute angle with positive direction of time axis represents positive acceleration while that inclined at an obtuse angle represents negative acceleration.

Equations of motion in one dimension can be derived by analytical method as well as from velocity – time graph. Equations of motion can be calculated for four different cases: velocity after time t, distance travelled in t seconds, velocity after travelling a distance, displacement in nth second.

The acceleration due to gravity is the acceleration of a body under the influence of the gravitational pull. SI unit of acceleration due to gravity is ms-2. Free fall is a case when a body is falling vertically downwards under the effect of gravity. Equations of motion for free fall can be found out by replacing the acceleration ‘a’ with acceleration due to gravity ‘- g’ in the equations of motion. Motion under gravity can be represented graphically through displacement – time graph and velocity – time graph. Few characteristics of motion under gravity are time taken to reach the highest point, total time of flight, maximum height reached by the body, velocity on reaching back and horizontal range.

Motion of a body on smooth inclined plane can be categorized into two ways: motion up an inclined plane and motion down an inclined plane. The value of acceleration can be found out for both the cases.

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