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 accelerationWhat is the highest speed that the car could have had such that the driver survived? Express your answer with the appropriate units.

It is given that, a driver can probably survive an acceleration of 50 g that lasts for less than 30 ms, but in a crash with a 50 g acceleration lasting longer than 30 ms, a driver is unlikely to survive.

Let v is the highest speed that the car could have had such that the driver survived. Using a = -50 g and t = 30 ms

Using first equation of kinematics as :

[tex]v=u+at[/tex]

In case of crash the final speed of the driver is, v = 0

[tex]0=u+at[/tex]

[tex]-u=at[/tex]

[tex]-u=-50\times 9.8\times 30\times 10^{-3}[/tex]

u = 14.7 m/s

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