Question

The robot is programed to travel along a line segment at a constant speed. If P represents the robot’s position at

any given time t in minutes:
PP = (240, 60) +t // 10 (100, 100),
a. What was the robot’s starting position?
b. Where did the robot stop?
c. How long did it take the robot to complete the entire journey?
d. Did the robot pass through the point (310, 130), and, if so, how long into its journey did the robot reach this
position?

Answer 1

a)
`P(0) = (240,60) + (0)/(10) (100,100)= (240,60)`

b)
`P(10) = (240,60) + (10)/(10) (100,100)= (240,60)+(100,100)= (340,160)`

c) We assume that the total travel takes 10 minutes since we have a entire length segment.

d) For this case we need to see if the robot passes thorugh the point (310,130) and we can do this, we need to see if for some time t between 0 and 10 we have the following equations:

`240 + (t)/(10) 100= 310`

`60 + (t)/(10) 100= 130`

If we solve for t we got:

`70 = 10 t`

`t = 7`

And for the second equation we have this:

`70 =10 t`

So for both equations we got te same solution t= 7 minutes so then the robot pased through the point (310,130) at t= 7 minutes.

Explanation:

for this case we have the following function who represent the position of the robot:

`P = (240,60) + (t)/(10) (100,100)`

Part a

The starting position correspond to t=0 and if we replace this we got:

`P(0) = (240,60) + (0)/(10) (100,100)= (240,60)`

Part b

We assume that the position is a linear function and the final time is t=10 so then if we assume that the motion ends at t=10 we have this:

`P(10) = (240,60) + (10)/(10) (100,100)= (240,60)+(100,100)= (340,160)`

Part c

We assume that the total travel takes 10 minutes since we have a entire length segment.

Part d

For this case we need to see if the robot passes thorugh the point (310,130) and we can do this, we need to see if for some time t between 0 and 10 we have the following equations:

`240 + (t)/(10) 100= 310`

`60 + (t)/(10) 100= 130`

If we solve for t we got:

`70 = 10 t`

`t = 7`

And for the second equation we have this:

`70 =10 t`

So for both equations we got te same solution t= 7 minutes so then the robot pased through the point (310,130) at t= 7 minutes.