Question

A particle moves along the y-axis so that at time t?0 its position is given by y(t)=t^3?4t^2+4t+3. Which of the following statements describes the motion of the particle at time t=1?

Answer 1

The statement "The particle is moving down the y-axis with decreasing velocity." describes the motion of the particle at time t=1 (option A)

Why is this correct?

The velocity of the particle moving along the y-axis, represented by the function
`\( y(t) = t^3 - 4t^2 + 4t + 3 \)`, is given by its derivative
`\( y'(t) = 3t^2 - 8t + 4 \)`.

At
`\( t = 1 \)`, substituting into the velocity equation:

`\( V(t) = 3(1)^2 - 8(1) + 4 = -1 \)`.

At
`\( t = 1 \)`, the velocity of the particle is -1 units per unit time along the y-axis.

Therefore The particle is moving down the y-axis with decreasing velocity (option A)

Complete question:

User

A particle moves along the y-axis so that at time (t) 2 ≥ 0 its position is given by y(t)=t^34t^2+4t+3. Which of the following statements describes the motion of the particle at time 1-1?

(A) The particle is moving down the y-axis with decreasing velocity.

(B) The particle is moving down the y-axis with increasing velocity.

(C) The particle is moving up the y-axis with decreasing velocity.

(D) The particle is moving up the y-axis with increasing velocity.