Motion in a plane involves the movement of an object in two dimensions—usually along the x-axis and y-axis. Here are some important formulas related to motion in a plane:

1. Chapter-4
Motion in a plane
Formulae
1.UNIT VECTOR
ˆ A
A
A


2 .Triangle and Parallelogram law of vector addition.
We will find its magnitude
𝑹 = 𝑨𝟐 + 𝑩𝟐 + 𝟐 𝐀𝐁𝐜𝐨𝐬 𝜽
And direction 𝛼 = 𝑡𝑎𝑛−1 𝐵 sin 𝜃
𝐴+𝐵 cos 𝜃
3. Resolution of Vector
 In two dimension
Vector A is resolved into two components along x and y axis
𝐴 = 𝐴𝑥
2
+ 𝐴𝑦
2
and direction 𝜃 = 𝑡𝑎𝑛−1 𝐴𝑦
𝐴𝑥
 In three dimension
Vector A is resolved into two components along x , y and axis 𝐴 =
𝐴𝑥
2
+ 𝐴𝑦
2
+ 𝐴𝑧
2
4. Dot Product or scalar product
5.Cross or Vector product
6. Instantaneous velocity
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2. 7. Instantaneous acceleration
8. Expression for velocity in a plane
9. Relative velocity in two dimensions
a.velocity of object A relative to that of B is :
b.velocity of object B relative to that of A is :
10. Projectile Motion
An object is being thrown with certain velocity or projected is called a
projectile. Such a projectile might be a football, a cricket ball, a baseball or
any other object.
 When a body is projected in horizontal direction
 Trajectory 𝑦 =
𝑔
2𝑢2
𝑥2
(Parabolic path)
 Time of flight 𝑇 =
2ℎ
𝑔
 Horizontal Range 𝑅 = 𝑢
2ℎ
𝑔
 When a body is projected at an angle 𝜃 with horizontal direction
 Trajectory 𝑦 = 𝑥 tan 𝜃 −
𝑔
2𝑢2𝑐𝑜𝑠2𝜃
𝑥2
(Parabolic path)
 Time of flight 𝑇 =
2𝑢 𝑠𝑖𝑛𝜃
𝑔
 Horizontal Range 𝑅 =
𝑢2𝑠𝑖𝑛2𝜃
𝑔
 Maximum Height H=
𝑢2𝑠𝑖𝑛2𝜃
2𝑔
11.Uniform Circular Motion
When an object follows a circular path at a constant speed, the motion of the object is
called uniform circular motion. The word “uniform “refers to the speed, which is
uniform (constant) throughout the motion.
a = v2
/R = ω2
r
ac = 4π2
ν2
r
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3. Thus, the acceleration of an object moving with speed v in a circle of radius r has a
magnitude v2
/R and is always directed towards the centre. This is why this
acceleration is called centripetal acceleration.
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