Question

The position of a particle is given as x(t) = cos(3t) - sin(4t). Find the acceleration of the particle at t = 0.

a) -9
b) 0
c) 1
d) 16

Answer 1

The acceleration of a particle with the position x(t) = cos(3t) - sin(4t) at t = 0 is -9 m/s². This is found by taking the second derivative of the position function, resulting in -9 m/s² when evaluated at t = 0.

Step-by-step explanation:

The position of a particle is given by x(t) = cos(3t) - sin(4t). To find the acceleration of the particle, we need to take the second derivative of the position function with respect to time. The first derivative of x(t) will give us the velocity, v(t), and the second derivative will give us the acceleration, a(t).

The first derivative, which is the velocity, is v(t) = -3sin(3t) - 4cos(4t). Taking the derivative again to find acceleration, a(t) = -9cos(3t) + 16sin(4t).

At t = 0, a(0) = -9cos(3×0) + 16sin(4×0) = -9×1 + 16×0 = -9.

Therefore, the acceleration of the particle at t = 0 is -9 m/s², which corresponds to choice a.