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Three start-ups Three cars, A, B, and C, start from rest
Chapter 4, Problem 79E(choose chapter or problem)
Three start-ups Three cars, A, B, and C, start from rest and accelerate along a line according to the following velocity functions:
\(v_{A}(t)=\frac{88 t}{t+1}\) \(v_{B}(t)=\frac{88 t^{2}}{(t+1)^{2}}\) \(v_{C}(t)=\frac{88 t^{2}}{t^{2}+1}\)
(a) After t=1 s, which car has traveled farthest?
(b) After t=5 s, which car has traveled farthest?
(c) Find the position functions for the three cars assuming that all cars start at the origin.
(d) Which car ultimately gains the lead and remains in front?
Questions & Answers
QUESTION:
Three start-ups Three cars, A, B, and C, start from rest and accelerate along a line according to the following velocity functions:
\(v_{A}(t)=\frac{88 t}{t+1}\) \(v_{B}(t)=\frac{88 t^{2}}{(t+1)^{2}}\) \(v_{C}(t)=\frac{88 t^{2}}{t^{2}+1}\)
(a) After t=1 s, which car has traveled farthest?
(b) After t=5 s, which car has traveled farthest?
(c) Find the position functions for the three cars assuming that all cars start at the origin.
(d) Which car ultimately gains the lead and remains in front?
ANSWER:Problem 79E
Three start-ups Three cars, A, B, and C, start from rest and accelerate along a line according to the following velocity functions:
a. After t = 1 s, which car has traveled farthest?
b. After t = 5 s, which car has traveled farthest?
c. Find the position functions for the three cars assuming that all cars start at the origin
d. Which car ultimately gains the lead and remains in front?
Answer;
Step 1 of 3 ;
Given velocity functions are : ,
and
.
- In this problem we need to find after t =1s, which car has traveled farthest.
At t = 1 seconds : =
= 44
=
=
= 22
=
=
= 44
Therefore , after t = 1s car A and car C has traveled farthest.
Step 2 of 3;
b) In this problem we need to find after t =5s, which car has traveled farthest.