A pedestrian is crossing a street where the speed limit is 35 mph. A vehicle col

Question

A pedestrian is crossing a street where the speed limit is 35 mph. A vehicle collides with the pedestrian. The pedestrian was in the middle of the lane. The vehicle skids a total distance of 70’ until it comes to rest, with the impact occurring at the halfway mark. The acceleration for this particular vehicle and tires stopping on this particular dry road is 24.15 ft/s/s. (This information is calculated from tables and can be verified by experiment.) The pedestrian will negligibly affect the speed of the vehicle. It can be assumed the pedestrian maintains a constant walking speed before the collision and that the impact occurred in the middle of first lane from the sidewalk.

Question: Who is more liable, the pedestrian or the driver?

Considerations (5 pts each)

a) What was the vehicle’s initial speed in mph?

b) Estimate a reasonable walking speed for a pedestrian.

c) Approximate how far would it be from the sidewalk to the center of the lane.

d) How fast was the car going at the time of impact?

e) About how far up the street was the vehicle when the person started walking?

f) If the car had been going exactly the speed limit, would the pedestrian have been able to walk the length of the lane without the car needing to slow down or the pedestrian needing to run?

g) If the car had been going exactly the speed limit and had slowed down after an appropriate perception/reaction time, would the pedestrian have been able to cross the lane before the car entered the crosswalk?

h) What would the speed of the car have been at impact If the car had been going exactly the speed limit and had slowed down after an appropriate perception/reaction time?

i) Compare the risk of injury at the different speeds in the previous two questions.

j) State your final decision and why.

Explanation / Answer

To answer who is more responsible must know how fast the vehicle was

We use kinematic equations

Vf2= Vo2+ 2 a X

X = 70'

a = - 35 m/h 5280'/1 m 1h/3600 s = -51.3 ft/s2

0 = Vo2 + 2aX Vo2 = -2aX Vo2 = 2 51,370 = 7182 (pie/s)2 Vo = 84.75 ft/s

The vehicle is speeding more than the velocity limit

. a) Vo = 84.75 ft/s 1 m/5280 ft 3600 s/ 1 h = 57.84 mph

. b) They say the pedestrian speed is constant so we need to know the width of lanes and the time to reach half.
We used for the calculus the vehicle information, the crash occurs at halfway

Vf2= Vo2+ 2 a X2 X2= 35 ft

Vf2 = 84.752 - 2 51.3 35 Vf2 = 3591.5 (ft/s)2 V1 = 59.92 ft/s

Vf = Vo – a t t = (Vo-Vf)/a t= (84.75 – 59.92)/51.3 t= 0.484 s

They are not information on the width of the lane, but a standard value is 8.2 ft (2.5 meter)

The speed of the pedestrian is

Vp = (8.2/2)/0.484 Vp = 8,47 ft/s

. d) Vc = 59.92 ft/s

. e) The vehicle begins to slow down to see the pedestrian starts to cross the street, so this distance is35 ft

.f) Vo = 35 m/h 5280 ft/1 m 1 h/ 3600 s = 51.3 ft/s

Vf2= Vo2+ 2 a X Vf= 0 X= ?

X = (Vf2 –Vo2)/ 2aX = (0 – 51.32)/(-2 51.3) X = 25.65 ft

Consequently the vehicle stops before hitting the pedestrian.

. j ) Blame it on the vehicle to go speeding

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