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The full question is below.

A car starts from rest and moves around a circular track of radius $32.0\,\text m$. Its speed increases at the constant rate of $0.500\,\text{m/s}^2$.
(a) What is the magnitude of its net linear acceleration $15.0\,\text s$ later?
(b) What angle does this net acceleration vector make with the car’s velocity at this time?

In this question, I think it already gives us the acceleration is $0.500\,\text{m/s}^2$, so the net linear acceleration should just be $0.500\,\text{m/s}^2$, right? So, what did the question actually ask for, since it does not even need to calculate?

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  • $\begingroup$ They want you to calculate the acceleration that the car has to experience to stay on the circular track in addition. Maybe the use of language in high school physics has changed over the years or I am unfamiliar with the English curriculum, but in general acceleration is acceleration. "net linear acceleration" is a meaningless term, unless we give a special direction vector onto which we want to project the actual acceleration vector. In this case there are two such special vectors: the radial and the tangential vector. The remainder is vector addition. $\endgroup$
    – FlatterMann
    Commented May 19, 2023 at 2:40
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    $\begingroup$ I also kind of confused because it seems that the "net linear acceleration" should be the tangential acceleration, but the tangential had already been given, it's kind of weird. $\endgroup$
    – Stanley
    Commented May 19, 2023 at 2:50
  • $\begingroup$ I think it's a poorly phrased question. I would calculate the total acceleration vector and hand that in. If somebody says "that's wrong", then they really need to explain what "net linear acceleration" is supposed to mean. $\endgroup$
    – FlatterMann
    Commented May 19, 2023 at 2:56
  • $\begingroup$ you just calculated it. $\endgroup$
    – JEB
    Commented May 19, 2023 at 3:03
  • $\begingroup$ @FlatterMann linear = longitudinal, radial = transverse. $\endgroup$
    – JEB
    Commented May 19, 2023 at 3:04

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There's one acceleration in the direction of motion (the $0.500m/s^2$) and another towards the center of the track (centripetal acceleration). Presumably the question asks for the magnitude of the vector sum of these two accelerations. This would also fit with the question in (b), since the result will not be in the direction of the car's velocity.

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