In this lesson, Professor John Zhu gives an introduction to position, velocity and acceleration. He explains the position function, velocity function and acceleration function. He then shows you several example problems.
After 20 days, the ship is traveling 12480 [km/hour]
Space probe Voyager 1's position relative to the Sun can be approximately described by x(t) = 61530 [km/hour] t + 1.8 * 1010 km. Using values from the previous problem, how long would it take that solar sail to achieve greater speed than Voyager 1?
We need to find when their speeds would be equal. We'll call Voyager 1 ship A, and the solar sail ship B.
vA(t) = [d/dt] (61530 [km/hour] t + 1.8 * 1010 km)
vA(t) = 61530 [km/hour]
From the previous problem we know that vB(t) = 26 [km/(hour2)] t
Now we set the two equal and solve for t
26 [km/(hour2)] t = 61530 [km/hour]
t = [61530/26] [km/hour] [(hour2)/km]
t ≈ 2366.5 hours
It would take approximately 2367 hours or 99 days for the solar sail to achieve greater speed.
An object's position at t ≥ 0 is given by x(t) = −9.8 t2 + 20t. Graph an overlay of the position, velocity, and acceleration of the object with t as the horizontal axis.
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Position Velocity & Acceleration
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.