Interactive LearningWare 4.1 reviews the approach taken in problems such as this one. A 1800-kg car is traveling with a speed of 14.0 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 36.9 m?

F = 4788 N

Explanation:

Because the car moves with uniformly accelerated movement we apply the following formula:

vf²=v₀²+2*a*d Formula (1)

Where:

d:displacement in meters (m)

v₀: initial speed in m/s

vf: final speed in m/s

a: acceleration in m/s²

Data

d=36.9 m

v₀=14.0 m/s m/s

vf = 0

Calculating of the acceleration of the car

We replace dta in the formula (1)

vf²=v₀²+2*a*d

(0) ² = (14) ²+2*a * (36.9)

- (14) ² = (73.8) * a

a = - (196) / (73.8)

a = - 2.66 m/s²

Newton's second law of the car in direction horizontal (x):

∑Fx = m*ax Formula (2)

∑F : algebraic sum of the forces in direction x-axis (N)

m : mass (kg)

a : acceleration (m/s²)

Data

m=1800 Fkg

a = - 2.66 m/s²

Magnitude of the horizontal net force (F) that is required to bring the car to a halt in a distance of 36.9 m:

We replace data in the formula (2)

-F = (1800 kg) * (-2.66 m/s²)

F = 4788 N