Question

The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds.

s(t) = t^4 - 98t^2 + 2401, t ≥ 0.
(A) Find the velocity at time t.

v(t) =
(B) What is the velocity after 3 seconds?

Velocity after 3 seconds =

Answer 1

The velocity function is v(t) = 4t^3 - 196t. The velocity after 3 seconds is -540 ft/s.

Step-by-step explanation:

The velocity of a particle is given by the derivative of the position function. So, to find the velocity function, we need to find the derivative of the given function s(t) = t^4 - 98t^2 + 2401.

Taking the derivative, we get v(t) = 4t^3 - 196t.

(B) To find the velocity after 3 seconds, substitute t = 3 into the velocity function: v(3) = 4(3)^3 - 196(3) = -540 ft/s.