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At the instant the traffic light turns green, a car that has been waiting at an intersection starts with a constant acceleration of 6 feet per second per second. At the same instant, a truck traveling with a constant velocity of 36 feet per second passes the car. (a) How far beyond its starting point will the car pass the truck?

Respuesta :

Answer:

d = 432 ft

Explanation:

Let say after time "t" the car will overtake the truck

so at this position the distance moved by car and truck will be same

so we will have

[tex]d_{car} = vt + \frac{1}{2}at^2[/tex]

[tex]d_{car} = 0 + \frac{1}{2}(6)t^2[/tex]

[tex]d_{car} = 3 t^2[/tex]

now the distance moved by the truck in the same time is given as

[tex]d_{truck} = vt[/tex]

[tex]d_{truck} = 36 t[/tex]

so we have

[tex]3 t^2 = 36 t[/tex]

[tex]t = 12 s[/tex]

so the distance move by the truck will be given as

[tex]d = 36\times 12[/tex]

[tex]d = 432 ft[/tex]

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