Question

The equation of motion of a particle is s = t³ - 27t, where s is in meters and t is in seconds. (Assume t ≥ 0.) Find the velocity and acceleration as functions of t.

Answer 1

The velocity of the particle as a function of time is v(t) = 3t² - 27 m/s, and the acceleration is a(t) = 6t m/s².

Step-by-step explanation:

The equation of motion for a particle is given as s = t³ - 27t, where s is in meters and t is in seconds. To find the velocity and acceleration as functions of time, we will need to differentiate the position function s(t) with respect to time.

• The velocity v(t) is the first derivative of the position function, so v(t) = ds/dt = 3t² - 27.
• The acceleration a(t) is the second derivative of the position function, or the first derivative of the velocity function, thus a(t) = dv/dt = d(3t² - 27)/dt = 6t.

Therefore, the velocity of the particle as a function of time is v(t) = 3t² - 27 m/s and the acceleration is a(t) = 6t m/s².