Question

To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 30.0 km/hr approaches a car stopped at the red light. When the truck is 228.9 meters from the car the light turns green and the car immediately begins to accelerate at 2.0 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

Answer:

110 km/hr(1000/3600) = 30.6 m/s

119 km/hr = 33.1 m/s

x position of truck = -211.7+ 30.6 t

v car = 2.3 t until v = 33.1

at t = 14.4 s and x = (1/2)(2.3)(14.4^2)

= 238 m

after that xcar = 238 + 33.1 (t-14.4)

so during car acceleration period:

d = Xcar - Xtruck = .5(2.3)t^2 - 211.7 + 30.6 t

or

d = 1.15 t^2 + 30.6 t - 211.7

does that have a minimum between t = 0 and t = 14.4?

I do not know if you do calculus, if not you will have to find the vertex of that parabola with completing the square

d(d)/dt = 0 at min = 2.3 t +30.6

t = 30.6/2.3 = 13.3 seconds to minimum d

then

d = 1.15(13.3^2) +30.6 t -211.7

= 22.3 meters

IF U LIKE MY ANSWER PLEASE GIVE BRAINLIEST