Question

Suppose that a particle moves according to the law of motion:

s(t) = t^2 - 5t + 30, 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 v(t) of a particle whose position is given by s(t) = t^2 - 5t + 30 is the first derivative of the position function, resulting in v(t) = 2t - 5. To find the velocity after 3 seconds, substitute t = 3 into the velocity equation, yielding a velocity of 1 m/s after 3 seconds.

Step-by-step explanation:

When analyzing the motion of a particle, we often deal with equations for position (s(t)), velocity (v(t)), and acceleration (a(t)). The velocity is the derivative of the position function with respect to time, and acceleration is the derivative of the velocity function with respect to time. For the given position function s(t) = t^2 - 5t + 30, the velocity can be found by taking the first derivative:

v(t) = ds/dt = 2t - 5

To find the velocity after 3 seconds, we substitute t = 3 into the velocity equation:

Velocity after 3 seconds = v(3) = 2(3) - 5 = 6 - 5 = 1 m/s