Answer:
The braking distance of the car is 40 m
Step-by-step explanation:
The two steps are;
1) Calculation (finding) of the initial kinetic energy , K.E., of the car
2) Calculation (finding) of the braking distance from the calculated K.E., of the car
The initial Kinetic energy of the car, K.E. = 1/2×m×v²
Where;
m = The mass of the car = 1,600 kg
v = The velocity of the car = 20 m/s
∴ K.E. = 1/2 × 1,600 kg × (20 m/s)² = 320,000 joules
2) The work done in stopping the car, W = The braking force, 'F' × The braking distance, 'd'
∴ W = F × d
Where;
F = The braking force = 8,000 N
d = The braking distance of the car
By energy conservation principle, the work, 'W', that is required to stop the car = The initial kinetic energy of the car, K.E.
∴ W = K.E. = 320,000 joules
Therefore, by substituting the known values for the variables, we have;
320,000 J = 8,000 N × d
∴ d = 320,000 J/(8,000 N) = 40 m
The braking distance of the car, 'd' = 40 m.