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 is 3t² - 27 and the acceleration is 6t.

Step-by-step explanation:

The concept of "functions of time" is commonly used in mathematics, physics, engineering, and various scientific disciplines. A function of time essentially describes how a quantity changes with respect to time.

The velocity is the first derivative of the position, and the acceleration is the first derivative of the velocity.

Velocity as a function of time:

• v(t) = s'(t) = d/dt(t³ - 27t)
• v(t) = 3t² - 27

Acceleration as a function of time:

• a(t) = v'(t) = d/dt(3t² - 27)
• a(t) = 6t