All Problems

Kinematics

Problem 1.19

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