Question

In a car crash, large accelerations of the head can lead to severe injuries or even death. A driver can probably survive an acceleration of 50g that lasts for less than 30 ms, but in a crash with a 50g acceleration lasting longer than 30 ms, a driver is unlikely to survive. Imagine a collision in which a driver’s head experienced a 50g acceleration. a. What is the highest speed that the car could have had such that the driver survived?

Answer 1

Answer:

14.7 m/s

Explanation:

During a crash, a car moving with some initial velocity comes to rest. This means the car undergoes a constant deceleration. So according to the question, we have

Given:

• v = final velocity of the car = 0 m/s
• a = acceleration of the car = $-50g = -50\times 9.8\ m/s^2 = -490\ m/s^2$
• t = time for which the crash occurs = 30 ms = 0.03 s

Let us assume that the maximum initial velocity of the car for which the driver still could survive on a crash be u.

During the crash, the car moves with a constant acceleration. so using the equation for a constant acceleration, we have

$v = u+at\\\Rightarrow u = v-at\\\Rightarrow u = 0-(-490)(0.03)\\\Rightarrow u =14.7$

Hence, the highest speed that the car could have had such that the driver survived is 14.7 m/s.

Answer 2

Answer:

The highest speed is 14.7 m/s

Explanation:

According to the data that the exercise gives, we have the following:

a = acceleration = -50*g

t = 30 ms = 0.03 s

if we use the equation:

v = u + a*t, where v = 30

replacing values ​​and clearing u:

u = (50 * 9.8)*0.03 = 14.7 m/s