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I'm having some difficulty in a physics question.

The question is:

To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 81.0 km/h approaches a car stopped at the red light. When the truck is 94.6 meters from the car the light turns green and the car immediately begins to accelerate at 2.80 m/s^2 to a final speed of 117.0 km/hr. How close does the truck come to the car assuming the truck does not slow down? How far from the stop light has the car travelled when the truck reaches its closest distance?

My answer so far:

First thing I did, I drew a position time graph with the car beginning its acceleration at the origin and the origin being when the light turns green. The truck's constant speed intercepts the position axis at -94.6 m.

Truck arrives at the lights: when t = 4.20 s

(The Eqn of the truck is y = 22.5x - 94.6)

Therefore the car is 25 m away from the lights when the truck arrives at the lights. (d = 1/2at^2)

The car reaches its final velocity (17.0 km/h or 32.5 m/s) 1450 m away from the lights. Or about 32.5 seconds after the light turns green.

I'm not sure on how to figure out how close the car gets. I started a table and calculated when each vehicle was at different time points, but this is getting time consuming and I am sure there is a simpler way.

Thanks for the assistance, any help would be greatly appreciated.

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# Homework Help: Motion Question

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