1.1.2 - Solving Word Problems Involving Distance and Velocity Flashcards
The alien Shaxxxt is flying around the solar system in his new Insight Driven Flying Saucer. The saucer starts off pretty slow, but it picks up speed quickly.
The position function for the saucer in miles is P (t) = 2e^2t where t is in minutes. What is Shaxxxt’s velocity when t = 6?
651019.17 miles per minute
Consider this graph of P’ (t).
At which t-value is P (t) the greatest?
t_3
A cartoon cat lights a bomb and tosses it into the air. The bomb is set to detonate in 8 seconds. The altitude of the bomb is given by the function P (t) = −9t ^2 + 72t with P (t) in feet and t in seconds. What is the altitude of the bomb when it explodes?
0 feet
A 3-egg omelette is hurled by a disgruntled customer over the side of a building. The distance of the omelette from the customer in feet is given by P(t) = 16t^2.
t is measured in seconds. The omelette will hit the ground in 5 seconds. With what velocity does the omelette hit the ground?
160 feet per second
A man driving a little red sports car is travelling along the highway. His position is given in miles by P (t) = 3000t ^2 + 40t, with t in hours. The speed limit is 70 mph. At what time does the man reach the speed limit
18 seconds
A physicist with too much time on his hands is trying to calculate a position function for Tabby, his pet slug. He sets up a camera to take a picture of Tabby’s initial position and her location at every even minute thereafter.
At t = 0, Tabby is at the starting point.
At t = 2, she is 4 inches away.
At t = 4, she is 8 inches away.
At t = 6, she is 12 inches away.
Which of the following functions is the best fit for Tabby’s position function?
PTabby(t) = 2t
A man standing on top of a cliff throws a nickel over the side. The nickel’s altitude is given by the function P(t) = -16t^2 +576, where t is in seconds. When will the altitude of the nickel equal zero?
t = 6
A cartoon cat lights a bomb and tosses it into the air. The bomb is set to detonate in 8 seconds. The position of the bomb is given by the function P(t) = -9t^2 +72^t with P(t) in feet and t in seconds. Where is the bombs highest point?
144 feet
Suppose the altitude of a particular bomb being dropped out of a plane is given by the equation p (t) = −4.9t^ 2 + 26t + 10, where t is in seconds and p is in meters. What is the initial velocity of the falling bomb?
26 m/sec
Suppose the altitude of a ball shot into the air is given by the equation p (t) = −4.9t ^2 + 49t, where t is measured in seconds and p is measured in meters. What is the velocity of the object when it strikes the ground?
-49 m/sec
