Question

Determine the stopping distances for an automobile going a constant initial speed of 95 km/h and human reaction time of 0.40 s:

(a) for an acceleration a = 3.0 m/s²
(b) for a = -6.0 m/s²

Options:
A) 45.6 m and 91.2 m
B) 22.8 m and 45.6 m
C) 91.2 m and 45.6 m
D) 45.6 m and 22.8 m

Answer 1

The stopping distances for an automobile can be calculated using the initial speed and reaction time. For an acceleration of 3.0 m/s², the stopping distance is 22.8 m. For an acceleration of -6.0 m/s², the stopping distance is 45.6 m.

Step-by-step explanation:

To determine the stopping distances for an automobile, we need to calculate how far the car travels during the reaction time and then add that to the stopping time. In this case, the initial speed of the car is 95 km/h and the reaction time is 0.40 s.

(a) For acceleration a = 3.0 m/s², the stopping distance can be calculated as:

Stopping distance = (initial speed × reaction time) + (0.5 × acceleration × (reaction time)^2)

Substituting the given values:

Stopping distance = (95 km/h × 0.40 s) + (0.5 × 3.0 m/s² × (0.40 s)^2)

Calculating the values:

Stopping distance = 22.8 m

(b) For acceleration a = -6.0 m/s², the calculation is the same:

Stopping distance = (95 km/h × 0.40 s) + (0.5 × -6.0 m/s² × (0.40 s)^2)

Calculating the values:

Stopping distance = 45.6 m