Question

Find the velocity, acceleration, and speed of a particle with the given position function:

r(t) = 5cos(t) + 4sin(t))

(a) velocity

(b) acceleration

(c) speed Incorrect

Answer 1

To find the velocity, acceleration, and speed of a particle with the given position function, take the derivatives of the position function with respect to time. The velocity function is -5sin(t) + 4cos(t), the acceleration function is -5cos(t) - 4sin(t), and the speed can be calculated by finding the magnitude of the velocity vector.

Step-by-step explanation:

To find the velocity, acceleration, and speed of a particle with the given position function, we need to take the derivative of the position function with respect to time. Let's start with the given position function: r(t) = (5cos(t) + 4sin(t))

a) The velocity function can be found by taking the derivative of r(t) with respect to t. v(t) = dr/dt = -5sin(t) + 4cos(t)

b) The acceleration function can be found by taking the derivative of v(t) with respect to t. a(t) = dv/dt = -5cos(t) - 4sin(t)

c) The speed of the particle can be found by calculating the magnitude of the velocity vector. speed(t) = |v(t)| = sqrt((-5sin(t))^2 + (4cos(t))^2)