The problem is as follows:

A crystal is moving on an horizontal plane $x-y$ by the given law: $r(t)=\left(12t\hat{i}+ct^2\hat{j}\right)\,m$ with $t$ being the time on seconds and $c$ a positive constant with given acceleration units. If for t=0 the radius of curvature is $4\,m$. Find the tangential acceleration for $t=2\,s$.

The given alternatives are:

$\begin{array}{ll}

1.&\frac{216}{37}\sqrt{37}\,\frac{m}{s^2}\\

2.&216\sqrt{37}\,\frac{m}{s^2}\\

3.&\frac{\sqrt{37}}{37}\,\frac{m}{s^2}\\

4.&\frac{72}{37}\sqrt{37}\,\frac{m}{s^2}\\

5.&\frac{144}{37}\sqrt{37}\,\frac{m}{s^2}\\

\end{array}$

I'm confused exactly how to tackle this problem:

It seems obvious that it is needed the value of $c$ because with that, then I could obtain an expression from where it can be taken its derivative consecutively and with that the acceleration.

But the thing is if I do plug in the initial condition from t=0

The whole equation becomes zero.

$r(t)=(12t\hat{i}+ct^2\hat{j})$

$r(0)=(12t\hat{i}+ct^2\hat{j}) = 0$

So what can be done here?.

I cannot assume that the radius of curvature $4$ will be the same for $t=2$.

Can somebody help me here?.

A crystal is moving on an horizontal plane $x-y$ by the given law: $r(t)=\left(12t\hat{i}+ct^2\hat{j}\right)\,m$ with $t$ being the time on seconds and $c$ a positive constant with given acceleration units. If for t=0 the radius of curvature is $4\,m$. Find the tangential acceleration for $t=2\,s$.

The given alternatives are:

$\begin{array}{ll}

1.&\frac{216}{37}\sqrt{37}\,\frac{m}{s^2}\\

2.&216\sqrt{37}\,\frac{m}{s^2}\\

3.&\frac{\sqrt{37}}{37}\,\frac{m}{s^2}\\

4.&\frac{72}{37}\sqrt{37}\,\frac{m}{s^2}\\

5.&\frac{144}{37}\sqrt{37}\,\frac{m}{s^2}\\

\end{array}$

I'm confused exactly how to tackle this problem:

It seems obvious that it is needed the value of $c$ because with that, then I could obtain an expression from where it can be taken its derivative consecutively and with that the acceleration.

But the thing is if I do plug in the initial condition from t=0

The whole equation becomes zero.

$r(t)=(12t\hat{i}+ct^2\hat{j})$

$r(0)=(12t\hat{i}+ct^2\hat{j}) = 0$

So what can be done here?.

I cannot assume that the radius of curvature $4$ will be the same for $t=2$.

Can somebody help me here?.

Last edited: