In a collision, a vehicle decelerates at #-65# #ms^-2# for #9.4# #s#. What was its initial velocity? What was its velocity after it had been decelerating for #3# #s#?

1 Answer
May 5, 2016

The initial velocity was #611# #ms^-1#, and after #3# #s# of deceleration the velocity was #416# #ms^-1#.

Explanation:

We know the final velocity, #v=0# #ms^-1#, the acceleration is #-65# #ms^-2# (the minus sign just means it is in the opposite direction to the initial velocity) and the time taken is #9.4# #s#.

#v=u+at#

Rearranging:

#u=v-at=0-(-65*9.4)=611# #ms^-1#

As a real value, this is improbable, since it is equivalent to about #2200# #kmh^-1# or #1367# #mph#, but it's what the question says.

We can use the same equation now to find the velocity after 3 seconds:

#v=u+at=611+(-65)*3=416# #ms^-1#

Note that #9.8# #ms^-2# is an acceleration of #1# #g#. The acceleration (deceleration) in this accident is about #6.6# #g#, which is enough to make someone pass out from the acceleration alone.