A particle moves along a straight line with velocity v, measured in meters per second, given by
v(t)=⎩⎨⎧4,8,6−t,0≤t<2,t=2,2<t≤5,
where t is measured in seconds.
a. Compute the particle’s net displacement on the time interval 0≤t≤5 by evaluating ∫05v(t)dt. Show how you account for the point t=2.
b. Determine the particle’s average velocity on [0,5]. Include a brief explanation of why the average velocity can be found even though v is not continuous at t=2. Express your answer in meters per second.