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4 May, 18:44

A car starts from rest and moves around a circular track of radius 37.0 m. Its speed increases at the constant rate of 0.440 m/s2. (a) What is the magnitude of its net linear acceleration 18.0 s later? (b) What angle does this net acceleration vector make with the car's velocity at this time?

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  1. 4 May, 20:04
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    a) 1.76 m/s²

    b) 75.5°

    Explanation:

    1. linear (tangential) acceleration a:

    a = 0.44m/s²

    2. speed v:

    v (t) = at

    3. radial acceleration α on a track with radius r:

    α (t) = v²/r = (at) ²/r

    α (18) = (0.44*18) ²/37 = 1.7 m/s²

    4. total acceleration |a|:

    |a| = √ (a²+α²) = 1.76m/s²

    5. angle Ф with v:

    tanФ = (α/a) = > Ф = 75.5°
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