To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 22.0 km/hr approaches a car stopped at the red light. When the truck is 117.3 meters from the car the light turns green and the car immediately begins to accelerate at 2.2 m/s2. How close does the truck come to the car assuming the truck does not slow down?

Question

To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 22.0 km/hr approaches a car stopped at the red light. When the truck is 117.3 meters from the car the light turns green and the car immediately begins to accelerate at 2.2 m/s2. 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?

Answer 1

22 km/hr = 6.11 m/s

so, at time t seconds after the light changes, the distance between the two vehicles is
1/2 * 2.2 t^2 - (-117.2 + 6.11t) = 1.1t^2 - 6.11t + 117.2
this has a minimum of 108.72 at t = 2.777
the car has covered 1.1*2.777^2 = ____ m