Sight Distance A serious crash is being investigated, in which a car slid off th

Question

Sight Distance A serious crash is being investigated, in which a car slid off the road at a curve and collided with a utility pole. The road has an 80km/h speed limit and a 65 km/h advisory speed sign on the curve. You have been asked to assess:

Part (a) Inspection of the damage to the vehicle and pole suggests that the car was still travelling at 20 – 30 km/h on hitting the pole. From skid marks on the road you determine that the car started braking 30 m prior to leaving the (level) road surface. Following this, it travelled a further 20 m down a 4% gradient grass shoulder before hitting the pole. Testing of the (wet) road surface and the car tyres indicates that the likely deceleration rate on the road surface was between 0.6 – 0.7 g. On the smoother grass surface, the estimated deceleration rate is between 0.3 – 0.4 g. For the range of estimated values given, determine the minimum and maximum possible initial speeds of the car, prior to skidding along the road and grass.

Explanation / Answer

The maximum speed limit on the road=80 Kmph

The advisory speed limit on the curve=65 Kmph

So let us assume the vehicle is moving with a maximum allowable speed of 70 kmph

As skidding takes place only when brake is applied, so the final velocity is zero

V2-u2=2aS

V=0

-u2=-2x0.6gx30

u=18.79m/s

u=67.6 KMPH (This indicates that he was travelling at more than allowable speed on curve)

On the grass

The maximum speed is the minimum speed which he is entering the grass and leaving the road=67.6 kmph

Braking distance=30m, here the distance travelled is 50m

Let us calculate this with equations of motion

V=0

u=?

a=0.3g

S=50m

-u2=-2x0.3x9.8x[30+20]

u=17.155 m/sec

u=61.75 KMPH

Maximum speed on the road=70 kmph-75 kmph (Assumed)

Minimum speed on the road=67.6 Kmph

Maximum speed on the grass=67.6 kmph

Minimum speed on the grass=61.75 Kmph

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