Find the car's average velocity (in m/sec) between t=3 and t=6 .

Question

A car drives down a road in such a way that its velocity (in m/sec) at time t (in sec) is

v(t)=t^1/2+1

Find the car's average velocity (in m/sec) between t=3 and t=6 .

Answer 1

The average velocity between t = 3 and t = 6 is the car's displacement in that time interval (i.e., ∫₃⁶ v(t) dt) divided by the elapsed time, i.e.,

1/(6 - 3) ∫₃⁶ v(t) dt = 1/3 ∫₃⁶ (t^1/2 + 1) dt = 1/3 (2/3 • t^3/2 + t )|₃⁶

.............................= 1/3 (2/3 • 6√6 + 6 - 2/3 • 3√3 - 3)

.............................= 1/3 (4√6 - 2√3 + 3)

.............................≈ 3.11m/sec