KINEMATICS

1. KINEMATICS
How objects move

2. DISTANCE AND DISPLACEMENT
 Displacement gives both the length and the direction of an object’s path from
its starting point. It is, therefore, a vector quantity. Displacement measures
the distance along a straight line between the start and the end of an
object’s motion. Displacement can be represented by arrows that are drawn
to the scale and point in a given direction.
 We define distance as the total length along a path between two points.
Distance is a scalar quantity.

3. SPEED AND VELOCITY
 Speed is one of the descriptors of motion. It describes how fast an object
moves. It is defined as the distance covered in a given time interval.
 Formula:
average speed =
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑜𝑣𝑒𝑟𝑒𝑑
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
or 𝑣𝑠 =
𝑑
𝑡
 Velocity is defined as the total displacement covered in a given time interval.
 Formula:
average velocity =
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
or v =
𝑑
𝑡

4. ACCELERATION
 When an object speeds up or slows down, it undergoes a change in its
velocity. As a result, it accelerates.
 Acceleration is the measure of how velocity changes with time.
 Formula:
 If an object slows down, its final velocity becomes less than its initial
velocity. The decrease in velocity is called deceleration.

5. UNIFORMLY ACCELERATED MOTION
 Uniformly means that something does not change.
 When an object is moving at constant acceleration along the straight line, the
motion of the object is described to be uniformly accelerated.
 Four equations of motions
𝑣𝑓 = 𝑣1 + at Where, t = time interval
d = 𝑣1t +
𝑎𝑡2
2
v = average velocity
𝑣𝑓
2
= 𝑣𝑖
2
+ 2ad 𝒗𝟏 = initial velocity
𝑣𝑎𝑣𝑒 =
𝑣1+𝑣𝑓
2
𝒗𝒇 = final velocity at any time t
a = constant acceleration

6. FREE FALL MOTION
 The motion of any falling objects is found to be under a constant acceleration
called the acceleration due to gravity g.
 Any motion that undergoes a constant acceleration equivalent to g is called
free fall motion.
 Formula:
𝑣𝑓 = 𝑣1 - gt
d = 𝑣1t +
1
2
𝑔𝑡2
𝑣𝑓
2
= 𝑣𝑖
2
- 2gd
𝑣𝑎𝑣𝑒 =
𝑣1+𝑣𝑓
2

7. PROJECTILE MOTION
 A projectile motion is any motion of an object which has an initial velocity
with a horizontal component and is acted upon by gravity.
 The total time of a projectile is calculated by the equation t =
2𝑑
𝑔
. The total
distance fallen is equal to 𝑑𝑦 =
1
2
𝑔𝑡2
 The horizontal displacement of the projectile is called range. Range, 𝑑𝑥, is
calculated by multiplying the constant horizontal velocity, 𝑣𝑥, by the time, t.
𝑑𝑥 = 𝑣𝑥t