Finding Distance with Constant Speed: Solving for m and b

Then solve for m.In summary, John is walking at a constant speed in front of a motion sensor and after 1 second, he is 2.5 meters away from the sensor. 2 seconds later, he is 4 meters away. The equation for the distance, d, in meters, in terms of time, t, in seconds, is d= mt+ b, where m is the slope and b is the d intercept. The slope represents the change in distance over the change in time, or the rate at which John is moving. The d intercept represents the initial distance from the sensor when John begins walking. To find the equation, we can use the given data points and solve for m and b. Using this
  • #1
Abdullah Qureshi
16
0
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?
 
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  • #2
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 ...
 
  • #3
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.
 

1. What is considered a constant walking speed?

A constant walking speed is typically defined as maintaining the same pace or velocity throughout the entire duration of the walk.

2. How does walking at a constant speed affect the body?

Walking at a constant speed can improve cardiovascular health, strengthen muscles, and increase endurance. It can also help with weight management and improve overall physical fitness.

3. Is it better to walk at a constant speed or vary the pace?

Both walking at a constant speed and varying the pace have their benefits. Walking at a constant speed is great for building endurance and improving cardiovascular health, while varying the pace can help burn more calories and challenge the body in different ways.

4. How can I maintain a constant walking speed?

To maintain a constant walking speed, it is important to focus on your posture and stride length. Keeping your head up, shoulders back, and swinging your arms can help you maintain a steady pace. Additionally, using a pedometer or fitness tracker can help you track your speed and make adjustments as needed.

5. Can walking at a constant speed help with mental health?

Yes, walking at a constant speed can have positive effects on mental health. It can help reduce stress and anxiety, improve mood, and increase energy levels. Additionally, walking outdoors in nature can have even greater benefits for mental well-being.

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