Question

The position function of a particle is given by s = t³ - 10.5t² - 2t, t≥0. When does the particle reach a velocity of 22 m/s?

Answer 1

To determine when the particle reaches a velocity of 22 m/s, differentiate the position function to find the velocity function and solve for t when v(t) = 22 m/s.

Step-by-step explanation:

The question asks when a particle reaches a velocity of 22 m/s, given its position function

s = t³ - 10.5t² - 2t, with t ≥ 0. To find when the particle reaches this velocity, we differentiate the position function to get the velocity function, which is

v(t) = ds/dt = 3t² - 21t - 2. We then set the velocity function equal to 22 m/s and solve for t to find when the particle reaches this velocity.

To solve v(t) = 22, we get the equation:
3t² - 21t - 24 = 0
This is a quadratic equation that can often be solved by factoring, using the quadratic formula, or using computational tools. Solving this equation provides the time(s) at which the particle reaches a velocity of 22 m/s.