Question

a particle moves in the $x - y$ plane, starting at the origin at time $t = 0$, with an initial velocity and constant acceleration given by: $vec{v}_{o}=a hat{i}+b hat{j}, quad vec{a}=c hat{i}$ with: $a = 5 \frac{m}{s}, b = 4.6 \frac{m}{s}, c = 0.6 \frac{m}{s^{2}}$ find the particles distance from the origin in meters at the time $t = 3s$. provide at least 1 decimal place

Explanation:

Step1: Find the x - coordinate

Use the kinematic equation \(x = v_{0x}t+\frac{1}{2}a_{x}t^{2}\). Here, \(v_{0x}=A = 5\frac{m}{s}\), \(a_{x}=C = 0.6\frac{m}{s^{2}}\), and \(t = 3s\).

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Step2: Find the y - coordinate

Use the kinematic equation \(y = v_{0y}t\). Here, \(v_{0y}=B = 4.6\frac{m}{s}\), and \(t = 3s\).

$$y=(4.6\times3)=13.8m$$

Step3: Find the distance from the origin

Use the distance formula \(d=\sqrt{x^{2}+y^{2}}\).

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Answer:

\(22.4\)