Determine the average rate of the train, in miles per hour, for the 3 hours Robert was traveling.
Answers
Step-by-step explanation:
calculate the speed at which the collision occurs:
Vf=V20−2ad−−−−−−−−√=8.2 metres per second
(where d = 40 metres minus the reaction distance of 27.1 metres = 12.9 metres).
Thus, the impact occurs at about 30 kilometres/hour, probably fast enough to kill Sam. If the car's initial speed was 70 kilometres/hour, the impact velocity would be 45 kilometres/hour, more than fast enough to kill.
These calculations assume that the driver has an average reaction time. If the driver is distracted and has a longer than average reaction time, then he or she may hit Sam without having applied the brakes at all.
IMPACT ON A PEDESTRIAN
Because the pedestrian, Sam, is so much lighter than the car, he has little effect upon its speed. The car, however, very rapidly increases Sam's speed from zero to the impact speed of the vehicle. The time taken for this is about the time it takes for the car to travel a distance equal to Sam's thickness—about 20 centimetres. The impact speed of Car 1 in our example is about 8.2 metres per second, so the impact lasts only about 0.024 seconds. Sam must be accelerated at a rate of about 320 metres per second per second during this short time. If Sam weighs 50 kilograms, then the force required is the product of his mass and his acceleration—about 16,000 newtons or about 1.6 tonnes weight.
Since the impact force on Sam depends on the impact speed divided by the impact time, it increases as the square of the impact speed. The impact speed, as we have seen above, increases rapidly as the travel speed increases, because the brakes are unable to bring the car to a stop in time.
Once a pedestrian has been hit by a car, the probability of serious injury or death depends strongly on the impact speed. Reducing the impact speed from 60 to 50 kilometres/hour almost halves the likelihood of death, but has relatively little influence on the likelihood of injury, which remains close to 100 per cent. Reducing the speed to 40 kilometres/hour, as in school zones, reduces the likelihood of death by a factor of 4 compared with 60 kilometres/hour, and of course the likelihood of an impact is also dramatically reduced.
Modern cars with low streamlined bonnets are more pedestrian-friendly than upright designs, such as those found in 4-wheel drive vehicles, since the pedestrian is thrown upwards towards the windscreen with a corresponding slowing of the impact. Cars with bull-bars are particularly unfriendly to pedestrians and to other vehicles, since they are designed to protect their own occupants with little regard for others.
IMPACT ON A LARGE OBJECT
If, instead of hitting a pedestrian, the car hits a tree, a brick wall, or some other heavy object, then the car’s energy of motion (kinetic energy) is all dissipated when the car body is bent and smashed. Since the kinetic energy (E) is given by
E=(1/2) mass×speed2
it increases as the square of the impact velocity. Driving a very heavy vehicle does not lessen the effect of the impact much because, although there is more metal to absorb the impact energy, there is also more energy to be absorbed.
LESS CONTROL
At higher speeds cars become more difficult to manoeuvre, a fact partly explained by Newton's First Law of Motion. This states that if the net force acting on an object is zero then the object will either remain at rest or continue to move in a straight line with no change in speed. This resistance of an object to changing its state of rest or motion is called inertia. It is inertia that will keep you moving when the car you are in comes to a sudden stop (unless you are restrained by a seatbelt).
To counteract inertia when navigating a bend in the road we need to apply a force—which we do by turning the steering wheel to change the direction of the tyres. This makes the car deviate from the straight line in which it is travelling and go round the bend. The force between the tyres and the road increases with increasing speed and with the sharpness of the turn (Force = mass × velocity squared, divided by the radius of the turn), increasing the likelihood of an uncontrolled skid. High speed also increases the potential for driver error caused by over- or under-steering (turning the steering wheel too far, thereby ‘cutting the corner’, or not far enough, so that the car hits the outside shoulder of the road).
KILLER SPEED
All these factors show that the risk of being involved in a casualty crash increases dramatically with increasing speed. In the University of Adelaide study referred to earlier, this was certainly true in zones where the speed limit was 60 kilometres/hour: the risk doubled with every 5 kilometres/hour above the speed limit. A corresponding decrease is to be expected in zones with lower speed limits.