A police car is traveling at a velocity of 18.0 m/s due east, when a car zooms b

Question

A police car is traveling at a velocity of 18.0 m/s due east, when a car zooms by at a constant velocity of 42.0 m/s due east. After a reaction time of 0.800 s the policeman begins to pursue the speeder with an acceleration of 5.00 m/s2.

a) Determine how far the speeder travels during the policeman's reaction time.
b) Determine how far the policeman travels during his reaction time.
c.) Using your results from a and b, determine how long it takes for the police car to catch up with the speeder once he starts to accelerate.

I'd appreciate any help with this problem. I'm confused. Thank you!

Explanation / Answer

SOLUTION: Speed of car, 42 m/s ( constant) Initial speed of poice car, 18 m/s,
Acceleration of police car, 5 m/s2 reaction time, 0.8 s (a) The speeder travels a distance during the policeman's reaction time, s1= (42 m/s)(0.8 s)     =33.6 m ____________________________________________________________ ____________________________________________________________ (b) The policeman travels a distance during his reaction time, s2=(18 m/s)(0.8 s)    =14.4 m ____________________________________________________________ ____________________________________________________________ (c) Let t be the time after which the police car catches the speeding car, So, the distance travelled by speeding car in time t is,
         st= (42 m/s )(t+0.8 s) Distance travelled by polc ecar,
         st= (18 m/s) (0.8) + (18 m/s )(t) + 0.5 (5 m/s2)t2 In order to the police car to catch up with the speeder, both the distances should have to be equal, Thus, equating these distances, we have (42 m/s )(t+0.8 s) = (18 m/s) (0.8) + (18 m/s )(t) + 0.5 (5 m/s2)t2 (2.5 m/s2) t2 + (18 m/s)t + (18 m/s)(0.8 s) - (42 m/s)t -(42 m/s)(0.8 s)=0 (2.5 m/s2) t2 + (18 m/s)t + (18 m/s)(0.8 s) - (42 m/s)t -(42 m/s)(0.8 s)=0 (2.5 m/s2) t2 -(24 m/s) t  - (19.2 m) =0 By solving this quadratic equation, we have the roots of t as t1 = 10.34 s and t2= -0.742 s Since, the - ve value of time not exist (excluded) consider the value of t is t1=10.34 s Thus, the polic ecar will catch the speedig car after time, (required time)        T=t +0.8 s           =10.34 s + 0.8 s           =11.14 s

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