Question

A particle projected from origin moves in x-y plane with a velocity v = 3i +6xj where i and j are the unit vectors along x and y axis. Find the equation of path followed by the particle

Answer 1

Answer on Question #44453, Physics, Mechanics | Kinematics | Dynamics

A particle projected from origin moves in $x-y$ plane with a velocity $v = 3i + 6j$ where $i$ and $j$ are the unit vectors along $x$ and $y$ axis. Find the equation of path followed by the particle

Solution:

We have

$$\mathbf{v}(t) = 3\mathbf{i} + 6\mathbf{j}$$

Integrating will give us the equation of path

$$\mathbf{r}(t) = \int \mathbf{v}(t) dt = \int (3\mathbf{i} + 6\mathbf{j}) dt = 3t\mathbf{i} + 6t\mathbf{j} + c$$

where $c$ is an arbitrary constant vector. Since the initial location is in origin.

This gives us $0 = \mathbf{r}(0) = \mathbf{c}$.

Thus,

$$\mathbf{r}(t) = (3\mathbf{i} + 6\mathbf{j})t$$

Answer: $\mathbf{r}(t) = (3\mathbf{i} + 6\mathbf{j})t$

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