Solved problem: Magnitude of the tangential acceleration

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Statement

difficulty

Knowing that the magnitude of the velocity of a body in S.I. units is:

$v = 7 + 2 \cdot t + 3 \cdot t^{2}$

Calculate the magnitude of the tangential acceleration.

Solution

Knowing that the tangential acceleration is obtained by the following expression:

$\vec{a_{t}} = \frac{d v}{d t} \vec{u_{t}} \Rightarrow |\vec{a_{t}}| = \frac{d v}{d t} |\vec{u_{t}}| \Rightarrow {|\vec{u_{t}}| = 1} \Rightarrow |\vec{a_{t}}| = \frac{d v}{d t} \Rightarrow |\vec{a_{t}}| = \frac{d (7 + 2 t + 3 t^{2})}{d t} \Rightarrow |\vec{a_{t}}| = 6 \cdot t + 2$

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

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{\vec{a}}_{t} = \frac{d v}{d t} {\vec{u}}_{t}

Tangential Acceleration

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Magnitude of the tangential acceleration

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Solution

Formulas worksheet