The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 1/(t^2), where t is measured in seconds.

Question

Find the velocity of the particle at t = a, t = 1, t = 2, and t = 3

Answer 1

Displacement as a function of time ( s(t) ) gives us the path that an object travels along (sometimes called its trajectory). By taking the time derivative of displacement, we get an expression for the object's velocity as a function of time ( v(t) ), and can evaluate it the same as displacement.

 

s(t) = 1/t² = t^-2

 

ds/dt = v(t) = -2*t^-3 = -2/t³

 

At the specified values of t:

 

v(a) = -2/a³

v(1) = -2/(1)³ = -2

v(2) = -2/(2)³ = -2/8 = -1/4

v(3) = -2/(3)³ = -2/27

Answer 2

How are velocity and displacement related?

 

Velocity is the derivative of the position function.

 

What is the derivative of s = 1/(t^2)?

 

Let's change it up a bit to make the function easier to see...

 

s = t^(-2)

 

What is the derivative of that? Use the power rule. Now you can find the velocities at all the given times.

 

I hope this helps!