1-d kinematics, physics question
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1-d kinematics, physics question

[From: ] [author: ] [Date: 12-06-27] [Hit: ]
So 30X+30=(1/2)3(x^2) Then just salve for x....Note* Both functions came from the same equation........
A car travelling at a constant speed of 30 m/s passes a police car hidden, one second after the speeding car passes the policeman the policeman sets of in pursuit at a constant acceleration of 3m/s. how long does it take the police car to catch the speed driver?
Note by the time the police set off in motion the speeding car has already travelled 30m

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The police car catches the speeding car
when the distances are equal:
Distance for speeder = v * t
Distance for police = 0.5 * a * (t^2)
So : v * t = 0.5 * a * (t^2)
And : t = v / (0.5 * a)
So : t = 30 / 1.5
t = 20 seconds + 1 second delay = 21 seconds

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Basically what you have here is two functions and you are looking for the point of intersection. The function for the constant speed car will be y=30x+30 and the function for the accelerating car will be y=(1/2)3(x^2). so to find the point of intersection you set them equal to each other.

So 30X+30=(1/2)3(x^2) Then just salve for x....

Note* Both functions came from the same equation... D=VT+(1/2)AT^2 Where D= distance V= initial velocity A= acceleration and T=time... To use this in a graph i used y as D and x as t... because it is a function of time. IN the first function we only used D=VT because the acceleration was 0. However you had to account for the extra 30m. so i moved the function 30 up... as seen here (f(X)+30). The second function was D=(1/2)AT^2 because the Initial velocity was 0.

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Let the distance travelled by speeding car is "x" till the police car catches it. So the distance travelled by police car is"x+30"
For Speeding Car x=30t (where t is the time taken to catch the speed driver)
and For Police Car x+30=1/2*3*t²
or 30t+30=3/2*t²
or 3t²=60t+60
or 3t²-60t-60=0
or 3(t²-20t-20)=0
or t²-20t-20=0
Solve the quadratic equation
1
keywords: physics,kinematics,question,1-d kinematics, physics question
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