Question

A particle moves along the x-axis so that at time t≥0, its position is given by x(t)=cos(t√). What is the velocity of the particle at the first instance the particle is at the origin?

a) -1
b) 0
c) 1
d) 2

Answer 1

The velocity of the particle at the first instance it is at the origin is approximately -1.57. Option A is correct.

Step-by-step explanation:

Given the position function x(t) = cos(t^2), we can find the velocity of the particle by taking the derivative of x(t) with respect to t. So, v(t) = -2t*sin(t^2).

To find the velocity of the particle at the first instance it is at the origin, we need to find the value of t when x(t) = 0. Setting cos(t^2) = 0, we get t^2 = (π/2)^2. Taking the square root on both sides, we get t = π/2 or t = -π/2.

However, since t≥0, the particle first reaches the origin at t = π/2.

Substituting t = π/2 into the velocity function, we get v(π/2) = -2*(π/2)*sin((π/2)^2) = -π*sin(π^2/4).

Therefore, the velocity of the particle at the first instance it is at the origin is approximately -1.57. So, the correct answer is (a) -1.