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 :
v₁ = 30 mph due east
v₂ = 60 mph due south
t = 4 hours
Unknown :
displacement = d = ?
Solution :
[tex]d_1 = v_1 \times t[/tex]
[tex]d_1 = 30 ~ mph \times 4 ~ h[/tex]
[tex]d_1 = \boxed {120 ~ miles}[/tex]
[tex]d_2 = v_2 \times t[/tex]
[tex]d_2 = 60 ~ mph \times 4 ~ h[/tex]
[tex]d_2 = \boxed {240 ~ miles}[/tex]
[tex]d^2 = (d_1)^2 + (d_2)^2[/tex]
[tex]d^2 = 120^2 + 240^2[/tex]
[tex]d^2 = 72000[/tex]
[tex]d = \sqrt{72000}[/tex]
[tex]d = 120\sqrt{5} ~ miles[/tex]
[tex]d \approx \boxed {268 ~ miles}[/tex]
Grade: High School
Subject: Physics
Chapter: Kinematics
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate
The Carrie and Brent are [tex]\boxed{268{\text{ miles}}}[/tex] apart from each other after 4 hours.
Further explanation:
The relationship between speed, distance and time can be expressed as follows,
[tex]\boxed{{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}}}[/tex]
Given:
Carrie drives due east at a rate of [tex]30{\text{ miles/hour}}.[/tex]
Brent drives due south at a rate of [tex]60{\text{ miles/hour}}.[/tex]
Explanation:
Consider the distance covered by the Carrie as [tex]{d_c}.[/tex]
The distance covered by the Carrie can be obtained as follows,
[tex]\begin{aligned}30&= \frac{{{d_c}}}{4}\\{d_c} &= 4 \times 30\\{d_c}&= 120{\text{ miles}}\\\end{aligned}[/tex]
Consider the distance covered by the Brent as [tex]{d_b}.[/tex]
The distance covered by the Brent can be obtained as follows,
[tex]\begin{aligned}60&= \frac{{{d_b}}}{4} \hfill\\{d_b} &= 4 \times 60 \hfill\\{d_b} &= 240{\text{ miles}} \hfill\\\end{aligned}[/tex]
The Carrie and Brent are [tex]\boxed{268{\text{ miles}}}[/tex] apart from each other after 4 hours.
Learn more:
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Speed
Keywords: Carrie, Brent, leave, same time, time, leave home, Carrie drives, east, rate, 30 mph, south, drive to south, 4 hours, 60 mph, far, apart,
