Solve the Problem $10 \mathrm {~cm}$ Back from Its Rest Position and Released at Time

question 317

Multiple Choice

Solve the problem.
-A small frictionless cart, attached to the wall by a spring, is pulled $10 \mathrm {~cm}$ back from its rest position and released at time $t = 0$ to roll back and forth for $4 \mathrm { sec }$ . Its position at time $t$ is
$\mathrm { s } = 1 - 10 \cos \pi \mathrm { t }$ . What is the cart's maximum speed? When is the cart moving that fast? What is the magnitude of of the acceleration then?

• A) \(10 \pi \approx 31.42 \mathrm {~cm} / \mathrm { sec } ; \mathrm { t } = 0.5 \mathrm { sec } , 1.5 \mathrm { sec } , 2.5 \mathrm { sec } , 3.5 \mathrm { sec }\); acceleration is \(0 \mathrm {~cm} / \mathrm { sec } ^ { 2 }\)
• B) \(\pi \approx 3.14 \mathrm {~cm} / \mathrm { sec } ; \mathrm { t } = 0.5 \mathrm { sec } , 1.5 \mathrm { sec } , 2.5 \mathrm { sec } , 3.5 \mathrm { sec }\); acceleration is \(0 \mathrm {~cm} / \mathrm { sec } ^ { 2 }\)
• C) \(10 \pi \approx 31.42 \mathrm {~cm} / \mathrm { sec } ; t = 0.5 \mathrm { sec } , 2.5 \mathrm { sec } ;\) acceleration is \(1 \mathrm {~cm} / \mathrm { sec } ^ { 2 }\)
• D) \(10 \pi \approx 31.42 \mathrm {~cm} / \mathrm { sec } ; \mathrm { t } = 0 \mathrm { sec } , 1 \mathrm { sec } , 2 \mathrm { sec } , 3 \mathrm { sec }\); acceleration is \(0 \mathrm {~cm} / \mathrm { sec } ^ { 2 }\)

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