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Equation of motion and two dimensional motion
Dr Manjunatha S
Kinematic Equation of motion of a
particle at constant acceleration:
Let consider,
v is final velocity of a particle,
u initial velocity of a particle,
a is acceleration of particle,
t is time taken by a particle and
s is the displacement of a particle.
(i) Velocity of a particle constant acceleration:
(ii) Average Velocity of a particle constant
acceleration:
(iii) Velocity of a particle after travelling
distance s at constant acceleration:
(iii) Distance
travelled by a particle after in
time interval at constant acceleration:
Problems:
1. A body starts from rest and acquires a
velocity of 12 m/s in 5 s. Calculate the
acceleration and distance moved by the body.
Example: 2,
A bus moving on a straight road with a speed of 126
km/h brought to rest after 200 m. Calculate
(A) acceleration of the bus and
(B) time taken by the bus to come to rest.
Example: 3
A car travelling at 9 m/s accelerate and attains a
speed of 27 m/s in 5 s. Calculate the acceleration
and distance covered in 5 s.
Motion in two dimension
Two dimensional motion of a particle is known
as the motion is in a plane.
The motion in two
dimensions are two
independent motions and
each of two perpendicular
directions are associated
with the x and y axes.
Position vector in the xy
plane can be written as
Position vector, 𝑟 = 𝑟1 + 𝑟2
Two dimensional equations
 Position
vector, 𝑟 = 𝑟1 + 𝑟2
 Displacement, 𝑟 = 𝑥 𝑖 + 𝑦𝑗
 Velocity, 𝑣
=
𝑑𝑥
𝑖
𝑑𝑡
 Acceleration, 𝑎
𝑑𝑦
+ 𝑗
𝑑𝑡
𝑑2𝑥
𝑑2𝑦
= 2𝑖+ 2𝑗
𝑑𝑡
𝑑𝑡
Example:1,
The position coordinates of a particle in a plane are (1,1)
and (2,3) at time t1 and t2 respectively. What are the
position vectors of the particle at t1 and t2 ? What is the
displacement of the particle during this time?
Example:2
The components of the velocity of a particle are
given by (4t - 2)m/s and (4t2-1) along x-axis and
y axis respectively. Calculate
A) The average acceleration of the particle
during the time interval from t=1 to t=2s and
B) The acceleration of the particle at t=2 s.