Question

The acceleration of a bus is given by ax (t) = at, where a = 1.2 m/s3.If the bus's velocity at time t = 1.0s is 5.0 m/s, what is its velocity at time t = 2.0 s?

Answer 1

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) = $\int\limits^2_1{a(t)}\,dt$

v(2) - 5 = $\int\limits^2_1{1.2t}\,dt$

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