A) We differentiate the expression for velocity to obtain an expression for acceleration: v(t) = 1 - sin(2πt) dv/dt = -2πcos(2πt) a = -2πcos(2πt)
b) Any value of t can be plugged in as long as it is greater than or equal to 0.
c) we integrate the expression of velocity to find an expression for displacement: ∫v(t) dt = ∫ 1 - sin(2πt) dt x(t) = t + cos(2πt)/2π + c x(0) = 0 0 = = + cos(0)/2π + c c = -1/2π x(t) = t + cos(2πt)/2π -1/2π
