i) The acceleration of a vehicle starting from rest and at position x = 0 (i.e., v(0) = 0 m/s and x(0) = 0 m) is as shown in the figure below: a(t), m/s x(t) i(1) 10 C -10 v(1) 2 a) Knowing that a(t) = dv/dt, sketch the velocity v(t). (5 points) b) Knowing that v(t) = dx/dt, sketch the position x(t) if the maximum position and the final position is x(8) = 100 m. (5 points) ii) A current is applied to a capacitor that has a capacitance C = 200 F (200 x 10-6 F) as shown in the figure below: i(t), A 8 2 t, s 8 t, ms dv(t) a) Knowing that i(t) = C dt sketch the voltage across the capacitor v(t). Note that the time is measured in ms and the initial voltage is zero (i.e., v(0) = 0). (5 points) b) Sketch the power if p(t) = i(t)v(t). (5 points)