v(2) = -9.8(2) + 20 = -19.6 + 20 = 0.4 m/s
s(t) = ∫v(t) dt = ∫(-9.8t + 20) dt = -4.9t^2 + 20t + C Integral Variable Acceleration Topic Assessment Answers
Integral variable acceleration refers to the process of using integration to find the position, velocity, or acceleration of an object when the acceleration is not constant. In other words, it involves finding the definite integral of the acceleration function to determine the change in velocity or position of an object over a given time interval. v(2) = -9
At t = 5
At t = 0, v(0) = 0, so C = 0.
v(t) = ∫a(t) dt = ∫(2t + 1) dt = t^2 + t v(t) = ∫a(t) dt = ∫(2t + 1)
s(t) = ∫v(t) dt = ∫(t^2 + t) dt = (1/3)t^3 + (1/2)t^2 + C