Question

Unreasonable results. A particle moves along the x-axis according to x(t)=3t3+5t​. At what time is the velocity of the particle equal to zero? Is this reasonable?

a) 1. t = 1 s; No, it's not reasonable.
b) 2. t = 0 s; Yes, it's reasonable.
c) 3. t = -1 s; No, it's not reasonable.
d) 4. t = 2 s; Yes, it's reasonable.

Answer 1

The velocity of the particle is never equal to zero in the given scenario.

Step-by-step explanation:

The velocity of the particle can be determined by taking the derivative of the position function. In this case, the position function is x(t) = 3t^3 + 5t. Taking the derivative, we get v(t) = 9t^2 + 5.

To find the time at which the velocity is zero, we set v(t) = 0 and solve for t. 9t^2 + 5 = 0. This equation has no real solutions, which means the velocity of the particle is never equal to zero. Therefore, none of the given options are correct or reasonable.