The position of an electron is given by r→=3.63ti^−5.73t2j^+8.16k^, with t in seconds and r in meters?

An electron's position is determined by #vecr=3.63thati−5.73t^2hatj+8.16hatk#Velocity #vecv# is first differential of position vector with time.v→=ddt(3.63ti^−5.73t2j^+8.16k^)⇒v→=3.63i^−11.46tj^(a) 3.63 ms−1(b) −11.46t ms−1 For t=2.63 s, we get−11.46×2.63=−30.140 ms−1(c) |v→|=(3.63)2+(−30.140)2|v→|=30.578 ms−1(d) If θ is the angle made by velocity with x-axis at time ttan⁡θ=vyvxInserting calculated valuestan⁡ θ=−30.1403.63, (4th quadrant)θ=−83.1∘, relative to the positive direction of the x-axis, in the desired range.

Question: "The position of an electron is given by..."

College
Physics
Advanced Physics

Jonas Bautista

Answered question

2022-12-25

The position of an electron is given by

\vec{r} = 3.63 t \hat{i} - 5.73 t^{2} \hat{j} + 8.16 \hat{k}

, with t in seconds and r in meters?

Answer & Explanation

inventivx64

Beginner2022-12-26Added 7 answers

An electron's position is determined by #vecr=3.63thati−5.73t^2hatj+8.16hatk#
Velocity #vecv# is first differential of position vector with time.

\vec{v} = \frac{d}{d t} (3.63 t \hat{i} - 5.73 t^{2} \hat{j} + 8.16 \hat{k})

\Rightarrow \vec{v} = 3.63 \hat{i} - 11.46 t \hat{j}

(a)

3.63 m s^{- 1}

(b)

- 11.46 t m s^{- 1}

For

t = 2.63 s

, we get

- 11.46 \times 2.63 = - 30.140 m s^{- 1}

(c)

| \vec{v} | = \sqrt{{(3.63)}^{2} + {(- 30.140)}^{2}}

| \vec{v} | = 30.578 m s^{- 1}

(d) If

θ

is the angle made by velocity with x-axis at time t

\tan θ = \frac{v_{y}}{v_{x}}

Inserting calculated values

\tan θ = \frac{- 30.140}{3.63}

, (4th quadrant)

θ = - {83.1}^{\circ}

, relative to the positive direction of the x-axis, in the desired range.

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