How to find tangential accel?

Question

https://i.stack.imgur.com/6U3uJ.png

I think this is a differentiate problem? How would I do this?

Just 0.3t^2 ? And then put the 5 in there? So answer is 15?

Answer 1

For part (c),

We have $\alpha \times r$

Here $\alpha = 0.6 rad/s^2$

And $r = 15 m$

Answer 2

$$(x(t),y(t))=(15\cos(0.3t^2),15\sin(0.3t^2))$$

So the velocity vector is $$\langle-9t\sin(0.3t^2),9t \cos(0.3t^2)\rangle$$ which has magnitude $9t$. So the tangential speed is $9t$ at time $t$, and the tangential acceleration is $\frac{d}{dt}9t=9$ (m/s^2).

Answer 3

You have $\theta=0.3t^2\implies \dot{\theta}=0.6t\implies \ddot{\theta}=0.6$

So for C, the tangential acceleration is $$r\ddot{\theta}=15\times0.6=9$$ And for D, the radial acceleration is $$r\dot{\theta}^2=15\times3.6^2=194.4$$