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Kinematics

Problem 1.19

A point traversed half a circle of radius \(R=160 \mathrm{~cm}\) during time interval \(\tau=10.0\) s. Calculate the following quantities averaged over that time: (a) the mean velocity \(\langle v\rangle\); (b) the modulus of the mean velocity vector \(|\langle\mathbf{v}\rangle|\) (c) the modulus of the mean vector of the total acceleration \(|\langle\mathbf{w}\rangle|\) if the point moved with constant tangent acceleration.

Reveal Answer
 (a) ⟨v⟩=πR/τ=50 cm/s (b) ∣⟨v⟩∣=2R/τ=32 cm/s (c) ∣⟨w⟩∣=2πR/τ2=10 cm/s2\text { (a) }\langle v\rangle=\pi R / \tau=50 \mathrm{~cm} / \mathrm{s} \text { (b) }|\langle\mathbf{v}\rangle|=2 R / \tau=32 \mathrm{~cm} / \mathrm{s} \text { (c) }|\langle\mathbf{w}\rangle|=2 \pi R / \tau^{2}=10 \mathrm{~cm} / \mathrm{s}^{2}
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