Question

Please show work

3. A car traveling at a constant 39 m/s (-87 mph) passes a police car that is initially traveling at 25 m/s (55 mph). At the instant of the pass, the police car accelerates at a constant rate of 3.3 m/s in pursuit. We wish to find how much time elapses before the officer catches the car. (a) Identify the initial states when the car passes the police. (b) Define the final state or conditions which enable you to answer the above question time

Answer 1

(a)Initial states

Speed of car ,$v_{c}=39m/s$

Speed of police car ,$v_{pc}=25m/s$

After the car passing,only the police car accelerate

so acceleration ,$a_{pc}=3.3m/s^{2}$

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(b)After certain distance d and time t police car catches the car

consider the car

speed =distance /time

$v_{c}=d/t$

$39m/s=d/t$

$39=d/t$

$39t=d$ -------------------(1)

Consider the police car

$d=ut+1/2at^{2}$

$d=25m/s*t+1/2*3.3m/s^{2}*t^{2}$

$d=25t+1/2*3.3*t^{2}$

$d=25t+1.65t^{2}$ ----------(2)

from(1)

$39t=25t+1.65t^{2}$

$14t=1.65t^{2}$

$14=1.65t$

ANSWER: ${\color{Red} t=8.485s}$

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