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xeze [42]
3 years ago
8

Being 10 miles apart, two cars started moving towards each other. After one hour they met, and during that time the first car co

vered 2 miles more than the second car. What was the speed of the first car?

Mathematics
2 answers:
Vladimir [108]3 years ago
7 0

The speed of the first car was 6 miles/hour

<h3>Further explanation</h3>

Acceleration is rate of change of velocity.

\large {\boxed {a = \frac{v - u}{t} } }

\large {\boxed {d = \frac{v + u}{2}~t } }

<em>a = acceleration ( m/s² )</em>

<em>v = final velocity ( m/s )</em>

<em>u = initial velocity ( m/s )</em>

<em>t = time taken ( s )</em>

<em>d = distance ( m )</em>

Let us now tackle the problem!

<u>Given:</u>

Distance between two cars = d = 10 miles

Time Taken = t = 1 hour

Distance covered by the first car = d₁ = 2 + d₂

<u>Unknown:</u>

Speed of the first car = v₁ = ?

<u>Solution:</u>

d = d_1 + d_2

10 = ( 2 + d_2 ) + d_2

10 = 2 + 2d_2

10 - 2 = 2 d_2

8 = 2 d_2

d_2 = 8 \div 2

d_2 = 4 \texttt{ miles}

\texttt{ }

d_1 = 2 + d_2 = 2 + 4 = 6 \texttt{ miles}

v_1 = d_1 \div t = 6 \div 1 = 6 \texttt{ miles/hour}

<h3>Learn more</h3>
  • Velocity of Runner : brainly.com/question/3813437
  • Kinetic Energy : brainly.com/question/692781
  • Acceleration : brainly.com/question/2283922
  • The Speed of Car : brainly.com/question/568302

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Kinematics

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

guapka [62]3 years ago
7 0

The speed of the first car is \boxed{6{\text{ mph}}} and the speed of the second car is \boxed{4{\text{ mph}}}.

Further explanation:

The formula of the speed can be expressed as follows,

\boxed{{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}}}

The formula of the time can be expressed as follows,

\boxed{{\text{Time}} = \frac{{{\text{Distance}}}}{{{\text{Speed}}}}}

Given:

The distance between the two cars is 10{\text{ miles}}.

The first car covered 2 miles more than the second car.

Explanation:

Consider the speed of the second car be “x”.

Consider the speed of the first car be “x+2”.

The distance covered by the first car in one hour is x + 2{\text{ miles}}.

The distance covered by the second car in one hour is x{\text{ miles}}.

The total distance covered by two cars is 10{\text{ miles}}.

\begin{aligned}x + 2 + x &= 10\\2x + 2 &= 10\\2x &= 10 - 2\\2x &= 8\\x&= 4\\\end{aligned}

The speed of the second car is 4{\text{ miles/h}}.

The speed of the first car can be obtained as follows,

\begin{aligned}{\text{Speed}} &= x + 2\\&= 4 + 2\\&= 6{\text{ miles/h}}\\\end{aligned}

The speed of the first car is \boxed{6{\text{ mph}}} and the speed of the second car is \boxed{4{\text{ mph}}}.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Speed and Distance

Keywords: 10 miles, speed of first car, speed of the second car, after one hour, moving toward, each other, 2 miles per hour, one hour.

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