The driver of a car moving at 90.0 km/h presses down on the brake as the car enters a circular curve of radius 195.0 m. If the speed of the car is decreasing at a rate of 4.0 km/h each second, what is the magnitude of the acceleration of the car (in m/s2) at the instant its speed is 58.0 km/h?

Approximately .

Explanation:

The acceleration on the car comes in two parts:

These two accelerations are perpendicular to each other.

Convert the current velocity to meters-per-second (.)

.

Convert the acceleration due to braking to meters-per-second-squared (.)

.

Calculate the acceleration due to the circular motion:

.

Since the two accelerations are perpendicular to each other, the resultant acceleration can be found using the Pythagorean Theorem

.

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