Motion and Constant Acceleration. A speeding car is traveling at a constant speed of #30.0m/s# when it passes a stopped police car. The police car accelerates at #7.0m/s^2#. How fast will it be going when it catches up with the speeding car?

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Answer 1 · 2018-02-24T15:36:09

The speed of the police car is #=60ms^-1#

To catch the speeding car, the distance travelled is the same by both cars,

For the speeding car,

#d=ut=(30t )"m"#

For the police car,

The initial speed is #u=0#

#d=ut+1/2at^2=0+1/2*7*t^2#

Therefore,

#30t=7/2t^2#

#30t-7/2t^2=0#

#t(30-7/2t)=0#

#t=0# which is the initial condition

#30-7/2t=0#, #=>#, #t=60/7s#

Therefore,

The speed of the police car is

#v=u+at=0+7*60/7=60ms^-1#