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(30) A motorist is driving at 15m when she sees that a traffic light 315 m ahead has just turned red. She knows that this light stays red for 25 s, and she wants to be 20m from the light when it turns green again. That way, she'll still be able to stop if the light stays red longer than expected. She applies the brake gradually such that her acceleration is a,(t) =c+ bt, where e and b are constants. Assume she starts with constant speed at the origin. Note: you will have to find the values of c, b, and any other unknown constants in order to answer the questions below. (a) Given the motorist's acceleration as a function of time, what are her position and velocity functions? You do not need to numbers for any of the constants here; you only need to derive her position and velocity functions. Show your work below. (b) What is her speed as she reaches the light?

(30) A motorist is driving at 15m when she sees that a traffic light 315 m ahead has just turned red. She knows that this light stays red for 25 s, and she wants to be 20m from the light when it turns green again. That way, she'll still be able to stop if the light stays red longer than expected. She applies the brake gradually such that her acceleration is a,(t) =c+ bt, where e and b are constants. Assume she starts with constant speed at the origin. Note: you will have to find the values of c, b, and any other unknown constants in order to answer the questions below. (a) Given the motorist's acceleration as a function of time, what are her position and velocity functions? You do not need to numbers for any of the constants here; you only need to derive her position and velocity functions. Show your work below. (b) What is her speed as she reaches the light?

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(30) A motorist is driving at 15m when she sees that a traffic light 315 m ahead has just turned red. She knows that this light stays red for 25 s, and she wants to be 20 m from the light when it turns green again. That way, she'll still be able to stop if the light stays red longer than expected. She applies the brake gradually such that her acceleration is a-(t) = c+ bt, where c and b are constants. Assume she starts with constant speed at the origin. %3D Note: you will have to find the values of c, b, and any other unknown constants in order to answer the questions below. (a) Given the motorist's acceleration as a function of time, what are her position and velocity functions? You do not need to numbers for any of the constants here; you only need to derive her position and velocity functions. Show your work below. (b) What is her speed as she reaches the light?
Transcribed Image Text:(30) A motorist is driving at 15m when she sees that a traffic light 315 m ahead has just turned red. She knows that this light stays red for 25 s, and she wants to be 20 m from the light when it turns green again. That way, she'll still be able to stop if the light stays red longer than expected. She applies the brake gradually such that her acceleration is a-(t) = c+ bt, where c and b are constants. Assume she starts with constant speed at the origin. %3D Note: you will have to find the values of c, b, and any other unknown constants in order to answer the questions below. (a) Given the motorist's acceleration as a function of time, what are her position and velocity functions? You do not need to numbers for any of the constants here; you only need to derive her position and velocity functions. Show your work below. (b) What is her speed as she reaches the light?
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