Question

A particle moves along the curve y=ax^3 such
that x=Bt, and A and B are constant,
Express the position vector of the particle in the lorm r(t) = xi^+ yj.^ Calculate the velocity
of the particle along this path at any instant.

Answer 1

Answer on Question #69193- Physics / Other

A particle moves along the curve $y = Ax^3$ such that $x = Bt$, and $A$ and $B$ are constant. Express the position vector of the particle in the form $\mathbf{r}(t) = x\mathbf{i} + y\mathbf{j}$. Calculate the velocity of the particle along this path at any instant.

Solution:

$$x(t) = Bt,$$ $$y(t) = Ax^3 = AB^3 t^3.$$

The position vector of the particle

$$\mathbf{r}(t) = x(t)\mathbf{i} + y(t)\mathbf{j} = Bt\mathbf{i} + AB^3 t^3\mathbf{j}.$$

The velocity of the particle

$$\mathbf{v}(t) = \mathbf{r}'(t) = x'(t)\mathbf{i} + y'(t)\mathbf{j} = B\mathbf{i} + 3AB^3 t^2\mathbf{j}.$$

**Answer**: $\mathbf{v}(t) = B\mathbf{i} + 3AB^3 t^2\mathbf{j}$

Answer provided by https://www.AssignmentExpert.com