Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a speed of 3.0 m/s and Betty has a speed of 2.0 m/s. Their dog, Spot, starts by Arthur's side at the same time and runs back and forth between them at 5.0 m/s. By the time Arthur and Betty meet, what distance has Spot run?

Let t be the time they both meet. When they meet they both have covered the distance between them.

Arthur with 3 m/s would have covered 3t m
Betty with 2 m/s would have covered 2t m

3t + 2t = 100
5t = 100
t = 100/5
t = 20 seconds.

Spot who is helplessly runing back and forth at 5 m/s would have done this for 20 seconds.

This distance covered by spot = 5m/s * 20s = 100m

Answer Link

johanrusli johanrusli · Answer 2 · 2019-08-21T05:10:48+02:00

The distance Spot has traveled is 100 m

Further explanation

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

Given:

distance = d = 100 m

Arthur's speed = v₁ = 3.0 m/s

Betty's speed = v₂ = 2.0 m/s

Spot's speed = v = 5.0 m/s

Unknown:

Spot's distance = s = ?

Solution:

At first we will find time when the two of them meet.

[tex]\text {Arthur's distance + Betty's Distance} = 100 ~ m[/tex]

[tex]v_1t + v_2t = 100[/tex]

[tex]3t + 2t = 100[/tex]

[tex]5t = 100[/tex]

[tex]t = 100 \div 5[/tex]

[tex]\boxed {t = 20 ~ seconds}[/tex]

Because Spot runs back and forth until these two people meet, then:

[tex]\text {Spot's Distance} = vt[/tex]

[tex]\text {Spot's Distance} = 5(20)[/tex]

[tex]\large {\boxed {\text {Spot's Distance} = 100 ~ m} }[/tex]

Learn more

Velocity of Runner : https://brainly.com/question/3813437
Kinetic Energy : https://brainly.com/question/692781
Acceleration : https://brainly.com/question/2283922
The Speed of Car : https://brainly.com/question/568302

Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle