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CALC Cars A and B travel in a straight line. The distance
Chapter 2, Problem 95P(choose chapter or problem)
Two cars, A and B, travel in a straight line. The distance of A from the starting point is given as a function of time by \(x_{A}(t)=\alpha t+\beta t^{2}\), with \(\alpha=2.60 \mathrm{~m} / \mathrm{s} \text { and } \beta=1.20 \mathrm{~m} / \mathrm{s}^{2} \text {. }\). The distance of B from the starting point is \(x_{B}(t)=\gamma t^{2}-\delta t^{3}\), with \(\gamma=2.80 \mathrm{~m} / \mathrm{s}^{2} \text { and } \delta=0.20 \mathrm{~m} / \mathrm{s}\).
(a) Which car is ahead just after they leave the starting point?
(b) At what time(s) are the cars at the same point?
(c) At what time(s) is the distance from A to B neither increasing nor decreasing?
(d) At what time(s) do A and B have the same acceleration?
Questions & Answers
QUESTION:
Two cars, A and B, travel in a straight line. The distance of A from the starting point is given as a function of time by \(x_{A}(t)=\alpha t+\beta t^{2}\), with \(\alpha=2.60 \mathrm{~m} / \mathrm{s} \text { and } \beta=1.20 \mathrm{~m} / \mathrm{s}^{2} \text {. }\). The distance of B from the starting point is \(x_{B}(t)=\gamma t^{2}-\delta t^{3}\), with \(\gamma=2.80 \mathrm{~m} / \mathrm{s}^{2} \text { and } \delta=0.20 \mathrm{~m} / \mathrm{s}\).
(a) Which car is ahead just after they leave the starting point?
(b) At what time(s) are the cars at the same point?
(c) At what time(s) is the distance from A to B neither increasing nor decreasing?
(d) At what time(s) do A and B have the same acceleration?
ANSWER:Step 1 of 5
The equation of motion of car A:
……………………………………………..(1)
The equation of motion of car B:
…………………………………………..(2)