Motion along a straight line by a car

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SUMMARY

The discussion focuses on expressing the velocity of a car using function notation in the context of motion along a straight line. The user seeks clarification on how to represent the question "When is the car going 70 mph" using the notation v(t). It is established that v(t) typically denotes velocity at time t, while s(t) represents the position function. The correct formulation to find when the car reaches 70 mph is to set the derivative of the position function, s'(t), equal to 70, resulting in the equation s'(t) = 70.

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  • Understanding of function notation in mathematics
  • Knowledge of derivatives and their application in motion
  • Familiarity with velocity and speed concepts
  • Basic calculus principles
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Nero1
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Part B of the following problem seems to be fairly straightforward, but I can't seem to understand it properly. I might be overthinking the problem entirely.

Would anyone be willing to help?
 

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(b) asks you to "use function notation" to express the question "When is the car going 70 mph". On the left side of the equal sign you have "v(t)". Were you given that or did you choose it? Often "v(t)" is used to indicate the speed or velocity at time t but there is nothing in the problem that defines v(t). The only thing defined here is s(t). The speed, at time t, is the derivative of that, s'(t). I would answer s'(t)= 70.
 

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