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MATHEMATICS - CASE STUDY SOLUTION

   

A spring-mounted slider moves horizontally. The displacement expression of the slider is

     s = 20 sin5t.

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

Let the velocity and acceleration of the slider be v and a, respectively. Let the time be t.

Since the first order derivative of the displacement with respect to time is velocity.

     v = ds/dt

Let θ = 5t, apply chain rule to calculate the velocity.

     

When time t = 2 sec,

     v = 100 cos5t = 100 cos10 cm/sec

As the second order derivative of the displacement with respect to time is acceleration.

     

Let θ = 5t, apply Chain Rule to calculate the acceleration.

     

When time t = 2 sec,

     s = -500 sin5t = -500 sin10 cm/sec2

     
    Discussion


Velocity


Acceleration

  In section Trigonometric Functions of Derivatives (I), the procedure of plotting derivative function is introduced. Now try to plot the acceleration according to the displacement diagram by yourself. Notice that the acceleration is the second derivative of the displacement. In order to plot acceleration function, the velocity function has to be plotted first.