Acar slows down at -5.00 m/s² until it comes to a stop after travelling 15.0 m. what was the initial speed of the car?
(unit = m/s)

According to kinematics this situation is described as a uniformly accelerated rectilinear motion. This means the acceleration while the car is in motion is constant.

Now, among the equations related to this type of motion we have the following that relates the velocity with the acceleration and the distance traveled:

  (1)

Where:

is the Final Velocity of the car. We are told "the car comes to a stop after travelling", this means it is 0.

is the Initial Velocity, the value we want to find

is the constant acceleration of the car (the negative sign means the car is decelerating)

is the distance traveled by the car

Now, let's substitute the known values in equation (1) and find :

   (2)

   (3)

Multiplying by -1 on both sides of the equation:

   (4)

   (5)

Finally:

>>>This is the Initial velocity of the car

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day