Answer to Question #203840 in Calculus for Ola

Question

The distance, x mm, moved by a particle is related to the time in seconds. We have

x = 1.2 sin(2t)

Find the distance travelled, the velocity and the acceleration of the particle at a time of t = 0.3 seconds.

Answer 1

$$x(t)=1.2\sin(2t)$$

$$v(t)=x'(t)=2.4\cos(2t)$$

$$a(t)=v'(t)=-4.8\sin(2t)$$

$$x(0.3)=1.2\sin(2(0.3))=1.2\sin(0.6) (mm)$$

$$\approx0.677571 (mm)$$

$$v(0.3)=2.4\cos(2(0.3))=2.4\cos(0.6) (mm/s)$$

$$\approx1.980805(mm/s)$$

$$a(0.3)=-4.8\sin(2(0.3))=-4.8\sin(0.6) (mm/s^2)$$

$$\approx-2.710284(mm/s^2)$$