We are given the acceleration of the bus as a function of time:
a(t) = 1.2t
Let the velocity also be a function of time v(t).
Since a(t) is the change of v(t) over time, we can use the fundamental theorem of calculus to determine the velocity at t = 2s, or v(2), given that:
a(t) = 1.2t
v(1) = 5
v(2) - v(1) = [tex]\int\limits^2_1{a(t)}\,dt[/tex]
v(2) - 5 = [tex]\int\limits^2_1{1.2t}\,dt[/tex]
v(2) - 5 = 0.6t² evaluated between t = 1 and t = 2
v(2) - 5 = 0.6(4) - 0.6(1)
v(2) = 1.8 + 5
v(2) = 6.8m/s
