MHB Finding Distance with Constant Speed: Solving for m and b

[Abdullah Qureshi]

John is walking at a constant speed in front of a motion sensor. After 1 s, she is 2.5m from the sensor, 2 s later, she is 4 m from the sensor.
a) Find an equation of in the form d=mt+b
b) Determine the slope and d intercept and explain what they mean
c) How far will John be from the sensor 5s after he begins walking?

 

[skeeter]

distance from the sensor is a function of time in seconds

$d(1) = 2.5 \, m$
$d(1+2) = d(3) = 4 \, m$

slope, $m = \dfrac{\Delta d}{\Delta t} \, m/s$

see what you can do from here ...

 

[HOI]

Equivalently, since you are told that d= mt+ b, when t= 1, d= 2.5, so 2.5= m+ b and when m= 3, d= 4 so 4= 3m+ b.

Solve the two equations, m+ b= 2.5 and 3m+ b= 4, for m and b. I suggest you subtract the first equation from the second to eliminate b.