Page 49 - Math SL HB Sem 2

Kinematics

Kinematics is a study of moving objects. The origin of the word is from Greek, which
means : cinema. In kinematics we are dealing with 3 basic quantities: displacement of an
object from a fixed origin, velocity of an object, and acceleration.
Velocity (m/s): - rate ofchange ofdisptacement, 4.
-dt
- involves direction of motion as well as the speed.

Acceleration (m2ls;: - rate ofchange ofvelocity, {.
dt
- vector quantity
Displacement: direction + distance ( e.g. a town is 120 km from Seremban in north-
westerly)
Difference between distance and displacement :
If a body travels 3 km from origin, then retums to the origin
Distance : 6 l<rn
Displacement: 0 km

Integralion and Kinematics Droblems

The area beneath the velocity - time graph produces distance traveled.
- -
similarly with the acceleration time graph, i.e. the area under the acceleration time
graph represents the velocity.
ds dv d2s dv
dt dr dt, ds

From graph below, the displacement over the interval t1 , t2 is given by
]
I
dt
Displacement=. = fl'7v refers to the signed area
' 11 { }
ffowever, the distance covered over the interval t1 t2 is given by
I , ]
Distance=x: -
fvat+ J2vdt { refers to the calculated area }

v

t2
S vdt
J
tl
t
(aO) t2 t