Question

A particle moving along the x-axis such that at any time t >= 0 its position at any time is given by s(t) = t + sin(t) 0 <= t <= 2π. When is the particle at rest?

A) t = 0
B) t = π/2
C) t = π
D) t = 3π/2

Answer 1

The particle is at rest when its velocity is equal to zero. To find the time when the particle is at rest, we need to find the time values when the velocity is zero. The particle is at rest at t = π.

Step-by-step explanation:

The particle is at rest when its velocity is equal to zero. To find the time when the particle is at rest, we need to find the time values when the velocity is zero. Since the position of the particle at any time t is given by s(t) = t + sin(t), we can find the velocity derivative by differentiating the position function with respect to time.

The derivative of s(t) with respect to t is v(t) = 1 + cos(t), which represents the velocity of the particle. To find when the particle is at rest, we set v(t) equal to zero and solve for t.

v(t) = 1 + cos(t) = 0

cos(t) = -1

t = π

Therefore, the particle is at rest at t = π, so the correct answer is C) t = π.