Question Type 1: Determining speed of an object for a given trajectory Exercises

An object travels on the path $\mathbf{r}(t) = (0,0,0) + t(2,2,1)$. What is its speed?

An object moves along the path $\mathbf{r}(t) = (2,-1,3) + t(4,0,-3)$. Calculate its constant speed.

For an object moving with constant velocity given by $\mathbf{r}(t) = (1,0,1) + t(8,7,2)$, find its speed.

Does the line $\mathbf{r}(t) = (0,0,0) + t(1,2,4)$ pass through $(7,14,28)$? If so, find $t$.

An object moves with $\mathbf{r}(t) = (4,-2,1) + t(-3,6,2)$. Calculate its speed.

An object follows $\mathbf{r}(t) = (2,1,-1) + t(3,4,5)$. Determine whether it passes through $(11,13,19)$, and find $t$ if it does.

Find the speed of an object moving along $\mathbf{r}(t) = (1,2,3) + t(0,5,-12)$.

Does the path $\mathbf{r}(t) = (1,0,1) + t(8,7,2)$ pass through the point $(17,14,5)$? If so, find the time $t$.

Given $\mathbf{r}(t) = (-3,5,0) + t(6,-2,1)$, determine the speed of the object.

For $\mathbf{r}(t)=(-1,2,4)+t(5,-1,3)$, does the object ever reach $(9,-3,13)$? Find $t$ or explain why not.

An object moves via $\mathbf{r}(t) = (3,-2,5) + t(-2,3,1)$. Determine whether it reaches $(-1,7,8)$, and find $t$ if so.

Determine whether $\mathbf{r}(t) = (5,5,5) + t(2,-3,4)$ passes through $(17,-1,21)$ and find the corresponding $t$ if it does.