Question

The position of a model train, in feet along a railroad track, is given by

Answer 1

Answer:

Part a) The speed is $2.5\frac{ft}{sec}$

Part b) After 4 seconds the trains is 24 ft along the track

Part c) $t=6\ sec$

Step-by-step explanation:

we have

$s(t)=2.5t+14$

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

$m=2.5\frac{ft}{sec}$

therefore

The speed is $2.5\frac{ft}{sec}$

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

$s(4)=2.5(4)+14=24\ ft$

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

$29=2.5t+14$

subtract 14 both sides

$29-14=2.5t$

$15=2.5t$

Divide by 2.5 both sides

$6=t$

rewrite

$t=6\ sec$