Kinematics

Question 1

Kinematics

Answer 1

The branch of physics that deals with objects in motion without considering the forces that cause the motion

Question 2

Motion

Answer 2

When a body does not change its position with time, we can say that the body is at rest, while if a body changes its position with time

Question 3

Translational (Linear) Motion

Answer 3

A type of motion in which all parts of an object move the same distance in a given time
-Rectilinear motion refers to motion along a straight line.
Ex: An object thrown in the air follows a parabolic trajectory.
-Curvilinear motion refers to motion along a curved path. can be circular, parabolic, or any other type of curve. Ex: A person walking in a straight line.

Question 4

Rotational Motion

Answer 4

When an object moves about an axis and different parts of it move by different distances in a given interval of time
Ex: A spinning top, a rotating wheel, or the Earth spinning about its own axis.

Question 5

Circular Motion

Answer 5

Motion that refers specifically to the motion of an object along a circular path.
-Can be uniform (constant speed) or non-uniform (changing speed).
-In circular motion, the object is moving around a fixed point
-Typically analyzed in terms of its tangential speed and centripetal acceleration.
Ex: A car moving along a curved road, or a planet orbiting the sun.

Question 6

Oscillatory (Vibratory) Motion

Answer 6

A specific periodic motion that involves the to and fro movement of a body

Question 7

Directions/Dimensions

Answer 7

-One Dimensional Motion is the motion of a particle moving along a straight line
-Two-dimensional Motion is a particle moving along a curved path in a plane
-Three-dimensional motion describes particles moving randomly in space

Question 8

Sate of Motion

Answer 8

-Uniform Motion: When a body travels equal distances in equal intervals of time
-Non-uniform Motion: When a body travels unequal distances in equal time intervals

Question 9

Displacement

Answer 9

The distance moved by a body in a specific direction
-d =df−di
-df: Final position
-di: Initial position
-d: Displacement
-d = (dx,dy)(for2Dmotion)
_________
-2D Magnitude ∣d∣ = /dx²+dy²
-d =( dx,dy,dz)(for3Dmotion)
______________
-3D Magnitude ∣d ∣= /dx² +dy²​+dz²​​
-d(t)=∫∫a(t)dt
​

Question 10

Velocity

Answer 10

The rate of change of displacement in a given direction
v = Δx = xf -xi = displacement
Δt tf - ti change in time
-v(t) = dx
d(t)​
-v(t)=∫a(t)dt

Question 11

Instantaneous Velocity

Answer 11

v = Δx
Δt

Question 12

Average Velocity

Answer 12

a = Δx = vf -vi
Δt = tf - ti

Question 13

Acceleration

Answer 13

The rate of change of velocity
a = change in velocity = (v - u)/2
time
a = dx = d2x
d(t) d2(t)​

Question 14

1st Equation of Motion

Answer 14

(1)a = v - u
t
(2)v = u + at

Question 15

2nd Equation of Motion

Answer 15

(1) s = (v + u)t -v = u + at
( t )
s = (u + at + u)t
2
s = (2u + at)t
2
s = ut + 1/2at²

Question 16

Third Equation of Motion

Answer 16

s = 1/2(u+v)t

a = (v-u), t = (v-u), s = (v+u)t
t a 2
s = (u+v )*(v-u)
2 a
s = (v² - u²), cross multiply
2a
2as = v² - u²
v² = u² + 2as

Question 17

Rotational Kinematics Formulas (4)

Answer 17

(1.)w = wi + at
(2).θ = θi +(1/2)(wi + w)t
(3).θ = θi + (wi)t + (at²)/2
(4).w² = wi² +2a(θ - θi)

Question 18

Equations of Motion Under Gravity (3)

Answer 18

When working with gravity
-(1). v = u + gt
-(2). H = ut + 1/2gt²
-(3). v² = u² + 2gH
When working against gravity
-(1). v = u - gt
-(2). H = ut - 1/2gt²
-(3). v² = u² - 2gH

Question 19

Projectile

Answer 19

A projectile is anything that is given an initial velocity and left to move on its own in the presence of a constant force field

Question 20

Properties of projectiles

Answer 20

Projectiles have both vertical and horizontal component which are independent of each other
-Acceleration due to gravity for the vertical component is g while that of the horizontal component is zero

Question 21

Free Falling Body

Answer 21

An object that moves under the influence of gravity only

Question 22

Vertical Component of Velocity

Answer 22

vy = uy ± gt,
uy = ysin(θ)

Question 23

Horizontal Component of Velocity

Answer 23

vx = ux +axt, ax = 0
ux = ucos(θ)

Question 24

Angle of Projection (θ)

Answer 24

The angle between the projection and the horizontal
tanθ = vy = usinθ - gt
vx ucosθ
θ = tan⁻¹(vy) = (usinθ - gt)
(vx) ( ucosθ )

Question 25

Trajectory

Answer 25

The path followed by the projectile
x = (ucosθ)t, —> t = x
ucosθ
y = uyt - 1/2gt² , uy = uSinθ,
y = usinθ(t) -1/2gt²
sub for t
y = usinθ( x ) -1/2g( x )²
(ucosθ) (ucosθ)²
tan = sinθ
cosθ
y=xtanθ - gx²
2(u²)(Cos²θ)(

Question 26

Maximum Height (H)

Answer 26

The distance between the highest point reached and the horizontal plane through the point of projection

v² = u² - 2gH
@ Hmax v = 0
0² = u² - 2gH
uy = usinθ
u² = 2gH
(usinθ)² = 2gH
u²sin²(θ) = 2gH
Hmax = u²sin²(θ)
2g

Question 27

Time of Flight (T)

Answer 27

Time taken by the projectile to move from its initial position to the final position along its path
v = u -gt, v=0 T = 2t
0 = u -gt -T = 2usin(2θ)
u = gt g
usinθ = gt
t = usinθ

Question 28

Horizontal Range(R)

Answer 28

The distance from the initial to the final position of the projection
R = uTcosθ, T = 2usinθ
g
R = u2usinθ*cosθ
g
R = u²sinθcosθ
g

(sin(A + B) =sinAcosB + cosAsinB)
(sin(θ + θ) =sinθcosθ + cosθsinθ)
sin2θ = 2sinθcosθ

R = U²Sin(2θ)
g