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Speed: It is the rate of change of distance with respect to time.
s = d / t
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Velocity: It is the rate of change of displacement with respect to time.
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Acceleration: It is the rate of change of velocity with respect to time.
a = (v – u) / t
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Non-uniform deceleration: It is when there are unequal decreases in velocity in equal intervals of time.
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Graphs can be used to study motion.
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d-t graph
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Speed is equal to the gradient of such a graph.
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s = (d2 – d1) / (t2 – t1)
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Example:
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s-t graph
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Acceleration is equal to the gradient of such a graph.
a = (s2 – s1) / (t2 – t1)
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Distance covered is equal to the the area under the graph.
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Example:
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Constant gradient or uniform speed or uniform acceleration is represented by a straight line.
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Acceleration can happen even when speed is constant if direction is changing.
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For an object going in a circle at constant speed, the resultant force is towards the center of the circle.
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Free-fall
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Without air
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Constant acceleration (of 10 m/s2 on Earth).
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Objects of different weights fall together.
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With air
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As the air resistance increases, the resultant force (of weight and air-resistance) decreases.
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As resultant force decreases, the acceleration also decreases (according to Newton’s Second Law of Motion).
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When the resultant force becomes zero, there is no acceleration and the body is said to be falling with terminal velocity.
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