Question

QAA: A city bus is stuck in stop-and-go traffic. Let’s say it is at rest at time 0, and we’ll say that its position at time 0 is 0 meters along the road. Its acceleration function is a(t)=0.8*sin(t) m/s^2.

i) What is its velocity function, v(t) ? What are its units?

ii) What is its position function, s(t) ? What are its units? Graph a(t), v(t), s(t) on t=[0 to 4pi]

iii) How far does it move in the first 2pi (6.28ish) seconds?

iv) Is it okay to answer part (iii) by saying “Its velocity at time 2pi is ___ m/s, so multiply that by 2pi seconds to get the total distance travelled”? Explain.

This exercise is important because it does some things that exercises 41-50 above don’t do:

• It asks us to go from accel to velocity to position, instead of just 1 step in that process, and
• We have to have details on what v(t) is doing at all time points, not just its initial and final values; the one-step problems might give the impression that we just do one big integral from start time to stop time and get a single number and we’re done.

Answer 1