Question

If the position of a particle is given by x = 20t – 5t³ , where x is in meters and t is in seconds, when if ever is the particle's velocity zero?

Answer 1

The particle's velocity is zero at t = √(4/3) s or approximately t = 1.1547 s.

Step-by-step explanation:

The position of the particle is given by the equation x = 20t - 5t³, where x is in meters and t is in seconds. The velocity of the particle can be found by taking the derivative of the position function, which gives v(t) = 20 - 15t². To find when the velocity is zero, we set v(t) = 0 and solve for t.

20 - 15t² = 0

15t² = 20

t² = 20/15

t² = 4/3

t = √(4/3) or t = -√(4/3)

Since time cannot be negative, we discard the negative solution. Therefore, the particle's velocity is zero at t = √(4/3) s or approximately t = 1.1547 s.