physics-motion in a straight line

kinematics

motion of objects without going into the causes of motion

rest

position doesn’t change wrt reference point

motion

position of object changes wrt reference point

distance

length of path traveled by an object (scalar)

displacement

shortest distance from initial to final

speed formula

s/t

km/h to m/s

x 5/18

average speed formula

total distance/total time

average speed if equal time intervals

(v1+v2)/n

average speed if distance and speed given

(s1+s2)/(s1/v1)+(s2/v2)

average speed if equal distance but different speed

2v1v2/v1+v2

instantaneous speed

speed at an instant of time

instantaneous speed formule

ds/dt

uniform speed

body covers equal distances in equal time

non uniform speed

body covers unequal distances in equal time

velocity

displacement/time

what can cause change of velocit

• direction change

• speed change

acceleration

rate of change of velocity

acceleration formula

delta v/delta t

velocity wrt derivative

first derivative of position so its dx/dt

acceleration wrt derivative

second derivative of position so d²x/dt²

equations of kinematics

• v=u+at

• s=ut+1/2 at²

• v²=U²+2as

displacement in nth second formula

sn=u+a/2 (2n-1)

retardation

rate of change of reducing speed

stopping time formula

u/a

stopping distance formula

u²/2a

relations bw speed and stopping distance

• s1/s2=(u1/u2)²

• is speed doubles stopping distance quadruples

value of g

9.8 m/s²

galileos rule of odd numbers

during free fall distance is1:3:5 or 5:15:25

time for free fall formula

(2h/g)^1/2

velocity at which ball reaches the ground

v=(2gh)^1/2

time of ascent / descent

u/g

time of flight

2u/g

maximum height

u²/2g

height when t given

h=(gt²)/8

height when body is projected upwards

½ g(t1t2)

time for object to fall when vertically projected from a height

(u+√u²+2gh)/g

time for downwords projected motion

=(u+√u²+2gh)/g