Question: A company uses a model train to simulate the motion of a train through the tunnel. They set up a straight piece of track, with 2 stations. The acceleration, a, in m/s^2, of the train t seconds after it leaves the first station is modelled by the equation:
a = Pi/8*cos*Pi/4*t
We need to find the velocity and displacement of the train t seconds after it starts.
And secondly how can we describe the trains motion, using a sketch????
To get the velocity and displacement functions, you just integrate twice.
∫ π/8 * cos(π/4 * t) dt = 1/2 sin(π/4 * t)
∫ 1/2 sin(π/4 * t) dt = -2/π cos(π/4 * t)
How can you describe the motion with a sketch? Well, that train oscillates, so that's a start.
El que pega primero pega dos veces.