A driver of a car traveling at #15.0# #m##/##s# applies the brakes, causing a uniform acceleration of #-2.0##m##/##s^2#. How long does it take the car to accelerate to a final speed of #10.0# #m##/##s#? How far has the car moved during the braking period?

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Answer 1 · 2018-04-12T06:17:17

The time is #=2.5s#. The distance is #=31.25m#

Apply the equation of motion

#v=u+at#

The initial velocity is #u=15ms^-1#

The final velocity is #v=10ms^-1#

The acceleration is #a=-2ms^-1#

The time is

#t=(v-u)/(a)=(10-15)/(-2)=2.5s#

Apply the equation of motion

#v^2=u^2+2as#

to calculate the distance

The distance is

#s=(v^2-u^2)/(2a)=(10^2-15^2)/(-2*2)=31.25m#