Determine the stopping distances for a car with an initial speed of 93 km/h and human reaction time of 3.0 s for the following accelerations.
(a) a = -4.0 m/s2
, but has changed from what was graded. m
(b) a = -8.0 m/s2
but has changed from what was graded. m
distance during reaction time: V*3 seconds
distance during slowing= Vi^2/2a
change Vi 93km/hr to m/s
and add the distances.
To determine the stopping distances for a car with different accelerations, we need to consider two factors: the human reaction time and the deceleration due to the braking force applied by the car.
The total stopping distance is calculated using the formula:
Stopping Distance = Reaction Distance + Braking Distance
The reaction distance is the distance covered by the car during the driver's reaction time. This is calculated using the formula:
Reaction Distance = Initial Speed × Reaction Time
The braking distance is the distance covered by the car while it is decelerating. This can be calculated using the formula:
Braking Distance = (Initial Speed^2) / (2 × Acceleration)
Now let's calculate the stopping distances for the given accelerations.
(a) For a = -4.0 m/s²:
Initial Speed = 93 km/h = (93 × 1000) / 3600 m/s = 25.83 m/s
Reaction Time = 3.0 s
Reaction Distance = 25.83 m/s × 3.0 s = 77.49 m
Braking Distance = (25.83 m/s)^2 / (2 × -4.0 m/s²) = 338.98 m
Stopping Distance = Reaction Distance + Braking Distance
Stopping Distance = 77.49 m + 338.98 m = 416.47 m
Therefore, the stopping distance for the car with an acceleration of -4.0 m/s² is 416.47 m.
(b) For a = -8.0 m/s²:
Initial Speed = 93 km/h = 25.83 m/s
Reaction Time = 3.0 s
Reaction Distance = 25.83 m/s × 3.0 s = 77.49 m
Braking Distance = (25.83 m/s)^2 / (2 × -8.0 m/s²) = 169.49 m
Stopping Distance = Reaction Distance + Braking Distance
Stopping Distance = 77.49 m + 169.49 m = 246.98 m
Therefore, the stopping distance for the car with an acceleration of -8.0 m/s² is 246.98 m.