the acceleration of a bus is given by ax(t)=at, where a=1.2m/s3. if the bus's velocity at time t=1.0s is 5.0m/s, what is its velocity at time t= 2.0?
?? see
https://www.jiskha.com/questions/1798825/The-acceleration-of-a-bus-is-given-by-ax-t-at-where-a-1-2-m-s3-If-the-buss
To find the velocity at time t=2.0 seconds, we can integrate the given acceleration function, ax(t)=at, with respect to time, from t=1.0s to t=2.0s.
First, let's find the constant of integration by substituting the given velocity at t=1.0s into the equation. We have:
v(1.0) = ∫[from 0.0 to 1.0] a*t dt
5.0 m/s = ∫[from 0.0 to 1.0] 1.2 t dt
Now, let's integrate:
5.0 m/s = [1.2 * (t^2 / 2)] [from 0.0 to 1.0]
5.0 m/s = (1.2 * (1.0^2 / 2)) - (1.2 * (0.0^2 / 2))
5.0 m/s = (1.2 * 0.5) - (1.2 * 0.0)
5.0 m/s = 0.6 m/s
Now, we have found the constant of integration, which is 0.6 m/s.
To find the velocity at t=2.0 seconds, we can integrate the acceleration function again:
v(2.0) = ∫[from 0.0 to 2.0] 1.2 t dt
v(2.0) = 1.2 ∫[from 0.0 to 2.0] t dt
v(2.0) = 1.2 * [(t^2 / 2)] [from 0.0 to 2.0]
v(2.0) = 1.2 * [(2.0^2 / 2)] - 1.2 * [(0.0^2 / 2)]
v(2.0) = 1.2 * (4.0 / 2) - 1.2 * 0.0
v(2.0) = 1.2 * 2.0 - 0.0
v(2.0) = 2.4 m/s
Therefore, the velocity of the bus at t=2.0 seconds is 2.4 m/s.