
MATHEMATICS  CASE STUDY



Introduction 
Springmounted Slider


Chuck built a springmounted slider to illustrate
simple harmonic motion to his son . He pushes the slider to
the left side, releases it and the slider starts to move in the horizontal
guide. He is curious about the velocity and acceleration
2 second after the slider starts moving.
What is known:
 The displacement of the slider is expressed by
s = 20 sin5t.
 The time, t, is 2 seconds






Questions 


What is the velocity and acceleration of the slider 2 seconds after it starts to move?






Approach 


 The first order derivative of the displacement with respect to time
is velocity, ds/dt = v.
 The second order derivative of the displacement with respect to time
is acceleration, d^{2}s/dt^{2} = a.
 The first order derivative of velocity with respect to time is acceleration,
dv/dt = a.




