During a collision a car is brought to rest from a velocity of 30ft/s in a distance of 3ft. Determine the acceleration factor

Question

I need to determine the acceleration factor, do I need to find time first and use the equation a=(v_f-v_i)/t? Or can I just use the acceleration factor equation f=|a/g|

Answer 1

Since you do not know the time, find the acceleration (assuming it is constant) from the kinematic relation

 

v_f² - v_i² = 2ax

 

a = acceleration

x = 3 ft

v_f = 0  [final speed; came to a complete stop]

v_i = 30 ft/s  [initial speed]

 

a = -v_i²/(2x) = -(30)²/[2(3)] ft/s² = -150 ft/s²

 

The negative sign means the acceleration is opposite the direction of motion.  Now you can get |a/g|, with g = 32 ft/s². 

 

You could also work this by first finding time, but that is a much longer solution.  The kinematic relation works best in this kind of problem where initial and final speeds, along with the acceleration distance, are known (as long as the acceleration is constant).