Kinematics, when I was a child, was a little too technical for me, and a little boring.
Back then, I would remember just busy jotting down notes but never really understanding them and absorbing the concepts behind them.
But hey, now that I am working, I finally found it interesting. It is something that is very fundamental in our technology nowadays.
Transportations were made easy: ships, trucks, cars, gondola, etc.When we are riding on airplane, have we tried to think about how the inventors were able to check the speed, time, velocity and acceleration as to how the plane should go? When we are on a moving car, have we asked as to how scientist and inventors could predict how fast the car can move with respect to time, in certain velocity and acceleration. Even the baseball's movement we can trace using Kinematics, and the much more complex Rocket launches in space. Falling from high points such as buildings and cliffs, we have also been able to calculate using Kinematics. In this way, we were able to use them and discover bungee jumping, going down from planes on parachute, calculating falling objects from the top of buildings, etc.
KINEMATICS
In particular, kinematics is a concept in physics involving motions. In fact, it is from the Greek word "kenesis" which means "moving". Terms involved in Kinematics : Scalar, vector, displacement, speed, acceleration, velocity.
Basic equations in kinematics:
1) vf = vi + at not included : x
2) x = vi t + (1/2)at^2
3) vf^2 - vi^2 = 2as not included : t
4) x = ( vf + vi) / 2 * t not included : a
also definitions such as
speed = a * t
speed = s / t (displacement over time)
acceleration, a = v / t
here vi = initial velocity
vf = final velocity
t = time
a = acceleration
s = displacement
Back then in college, I would remember, having to check other key points and techniques to remember the formulas such as these:
- difference of squares of v is (2as)
- vf = VIAT because of (vi + at)
- x = (average of v's) * t since v (ave) = ( vi + vf)/2
- x = integral of v, is s. Integration of formula for v, with respect to t, from vi t + at becomes vi t + 1/2 at^2
Below are list of sample problems I have:
1) How long will it take for a car starting at rest and a = 5 m/s^2 to get 200 m?
Given: a = 5 m/s^2
s = 200 m
hidden given: vi = 0 starting at rest
Asked: t = ?
Solution:
x = vi * t + 1/2 ( at^2 ) Applicable equation with have a and s.
since vi = 0,
x = 1/2 at^2
200 = 1/2 ( 5 ) t^2
t = 9 sec.
2) A rock is dropped at 30 m/s. How high is the cliff?
Given: vf = 30/s
hidden given: vi = 0
Asked: s = ? or height h = ?
Solution:
vf^2 - vi^2 = 2 a s
Since this is free fall, a = g which is 9.8 m/s
vf^2 - vi^2 = 2 (-g) h
h = v i^2 / (2g)
h = (30)^2 / 2 (-g)
h = 45 m/s
3) A stone is thrown horizontally at vi = 30 m/s. What is the total speed after 4 sec.
speed?
Given: vi = 30 m/s
t = 4 sec
hidden given: projectile motion (throwing horizontally)
still use a or g = -9.8 m/s^2
Asked: Total speed, needs also vf = ?
Solution: Since speed, vf = g * t
At t = 4 with g = 9.8 m/s^2, vf = 40 m/s
total speed = vi + vf
= 30 m/s + 40 m/s
total speed = 70 m/s
4) A race car starts at a = 5 m/s^2. What is velocity after 1.0 x 10^2 ft or 100 ft? How much time?
Given: a = 5 m/s
s2 = 100 ft or 30.2 m/s
hidden given: vi = 0 since car starts at rest
Asked : vf = ? t = ?
Solution:
vf^2 - vi^2 = 2
vf^2 = 2 (5)(30 m/s) = 300
vf = 17.32 m/s
v = vo + at
17.32 = (5) t
t = 3.4 sec
Additional example:
A soccer ball at rest is kicked with vf = 10 m/s t 30 degrees. Calculate time.
First, list down all the given and unknown
vi = 10 m/s
hidden given: from ball at rest, vi = 0
hidden constant for projectile motion: a or g = 9.8 m/s^2
t = 2 ( v / a ) but in this case a = g
t = 2 v sin (theta) / g (for projectile)
t = 1.01 sec
Kinematics is indeed a challenging subject to handle, but we can manage if we understand how it was derived to form all equations.
