Question

A(n) 1555.4 kg car is coasting along a level road at 40 m/s. A constant braking force is applied, such that the car is stopped in a distance of 55.6 m. What is the magnitude of the braking force? Answer in units of N.

Answer 1

F= 22397.76 N : Magnitude of the braking force

Step-by-step explanation:

Kinematic analysis

Because the car move with uniformly accelerated movement we apply the following formulas:

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

v₀ = 40 m/s

vf = 0

d=55.6 m

We replace data in the formula (1)

vf²=v₀²+2*a*d

0 = (40)²+2*a*(55.6)

- (40)² = 111.2 *a

a = - (40)² / 111.2

a = - 14.4 m/s²

Kinetics

We apply Newton's second law:

∑F = m*a Formula (2)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Data:

a = - 14.4 m/s²

m = 1555.4 kg

We replace data in the formula (2)

F = m*a , F: braking force

-F = 1555.4 kg ( - 14.4 m/s² )

F= 22397.76 N : Magnitude of the braking force