At a given instant, a car on a roller coaster has velocity vector r′ = 〈25, −35, 10〉 (in miles per hour). What would the velocity vector be if the speed were doubled? What would it be if the car’s direction were reversed but its speed remained unchanged?
Two cars travel in the same direction along the same roller coaster (at different times). Which of the following statements about their velocity vectors at a given point P on the roller coaster is/are true?
The velocity vectors are identical.
The velocity vectors point in the same direction but may have different lengths.
The velocity vectors may point in opposite directions.
A mosquito flies along a parabola with speed υ(t) = t2. Let L(t) be the total distance traveled at time t.
How fast is L(t) changing at t = 2?
Is L(t) equal to the mosquito’s distance from the origin?
What is the length of the path traced by r(t) for 4 ≤ t ≤ 10 if r(t) is an arc length parametrization?