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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Definitions:

Stator Unit

The stationary part of an electric machine, such as a motor or generator, which works in conjunction with the rotor to induce motion or generate electricity.

Energizes

The act of supplying electrical power to a circuit or component, causing it to operate.

Motor Load

A measurement referring to the mechanical output power demanded from an electric motor, reflecting the resistance or work the motor must overcome.

Manual Motor Starters

Devices used to manually start and stop motors, providing protection against overloads by breaking the circuit.