Answer:
Part a) The speed is [tex]2.5\frac{ft}{sec}[/tex]
Part b) After 4 seconds the trains is 24 ft along the track
Part c) [tex]t=6\ sec[/tex]
Step-by-step explanation:
we have
[tex]s(t)=2.5t+14[/tex]
This is the equation of a line in slope intercept form
where
s(t) is the position of a model train in feet
t is the time in seconds
Part a) How fast is the train moving?
The speed of the train is equal to the slope of the linear equation so
The slope m is equal to
[tex]m=2.5\frac{ft}{sec}[/tex]
therefore
The speed is [tex]2.5\frac{ft}{sec}[/tex]
Part b) Where is the train after 4 seconds?
For t=4 sec
substitute the value of t in the equation and solve for s
[tex]s(4)=2.5(4)+14=24\ ft[/tex]
therefore
After 4 seconds the trains is 24 ft along the track
Part c) When will the train be 29 feet along the track?
For s(t)=29 ft
Substitute the value of s(t) in the equation and solve for t
[tex]29=2.5t+14[/tex]
subtract 14 both sides
[tex]29-14=2.5t[/tex]
[tex]15=2.5t[/tex]
Divide by 2.5 both sides
[tex]6=t[/tex]
rewrite
[tex]t=6\ sec[/tex]
