
Speed: It is the rate of change of distance with respect to time.
s = d / t

Velocity: It is the rate of change of displacement with respect to time.

Acceleration: It is the rate of change of velocity with respect to time.
a = (v – u) / t

Nonuniform deceleration: It is when there are unequal decreases in velocity in equal intervals of time.

Graphs can be used to study motion.

dt graph

Speed is equal to the gradient of such a graph.


s = (d_{2} – d_{1}) / (t_{2} – t_{1})

Example:


st graph

Acceleration is equal to the gradient of such a graph.
a = (s_{2} – s_{1}) / (t_{2} – t_{1})

Distance covered is equal to the the area under the graph.

Example:



Constant gradient or uniform speed or uniform acceleration is represented by a straight line.

Acceleration can happen even when speed is constant if direction is changing.

For an object going in a circle at constant speed, the resultant force is towards the center of the circle.

Freefall

Without air

Constant acceleration (of 10 m/s^{2} on Earth).

Objects of different weights fall together.


With air

As the air resistance increases, the resultant force (of weight and airresistance) decreases.

As resultant force decreases, the acceleration also decreases (according to Newton’s Second Law of Motion).

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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