Question

A particle moves according to the laws of motion s=f(t), t≥0, where t is measured in seconds and s in feet.

f(t) = sin(πt/2)
Find velocity at time t.
v(t)=__

Answer 1

The velocity of a particle expressed as v(t) = sin(πt/2) is found by differentiating the position function, resulting in v(t) = (π/2)cos(πt/2), which gives the velocity at any time t.

Step-by-step explanation:

The velocity of a particle is given by the equation v(t) = sin(πt/2). To find the velocity at time t, we need to take the derivative of the position function s with respect to time t.

Velocity is the first derivative of position. Using the chain rule for the derivative of the sine function, we have:

v(t) = d/dt[sin(πt/2)]
= (π/2)cos(πt/2)

This equation gives us the velocity v(t) of the particle at any time t.