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Acceleration of blood in vasculature; elevator springs energy

See attached file for the diagram.

1. The diagram shows the acceleration of blood in the vasculature versus time in seconds. Give the time at which the blood is moving with the maximum velocity. Explain your answer.

2. All modern elevators feature safety mechanisms. For example, if an elevator cable breaks, the falling elevator car will land on a set of giant springs on the bottom of the shaft, compressing them. However, the conservation of energy asserts that the energy required to break the car's fall is the same whether the springs are present or not. How, then, do the springs save lives? (Be specific - what quantities are changed when the springs are present? Which of these explains the difference?)


Solution Preview

1. Acceleration a = dv/dt.

Velocity v = Integral of adt = Area under the curve for a given infinitesimally small time duration

Hence, velocity of blood at any given instant is given by the area under the a vs t graph.

Let us take a time duration of 1 sec and see at which second the area under the given graph in maximum. It is obvious that the area under the graph is maximum during the 2nd second. Hence, ...

Solution Summary

The acceleration of blood in vasculature and the elevator springs energy is examined.