Question

Calculate the velocity and acceleration vecdtors at t = 1 of r(t) = and then find the speed at t = 1

Answer 1

Differentiate component-wise.$$\mathbf{r}'(t)=\left(2\cos2t,2\sin2t,\frac1{2\sqrt{t-1}}\right)\\\mathbf{r}''(t)=\left(-2\sin2t,2\cos2t,-\frac1{4\sqrt{(t-1)^3}}\right)$$Now evaluate at \(t=1\) for your velocity and acceleration vectors. Do you know how to determine the speed?

Answer 2

oops$$\mathbf{r}''(t)=\left(-4\sin2t,4\cos2t,-\frac1{4(t-1)^\frac32}\right)$$

Answer 3

To determine speed, isn't that the magnitude?

Answer 4

of which vector?

Answer 5

The velocity one!

Answer 6

AKA 1st derivative

Answer 7

Am I right @oldrin.bataku

Answer 8

Indeed!