Answer:
Halfway between B and A on the return leg.
Explanation:
Your average SPEED for the entire trip will equal your constant speed as the time and distance increase at proportionate rates.
Your average VELOCITY will equal your constant speed while you travel from A to B because time and displacement are increasing at proportionate rates.
When you turn around at B to return, your Displacement is now decreasing while your travel time continues to increase, so your average velocity decreases.
Lets say the distance from A to B is 90 km and your constant speed is 30 km/hr.
your average speed is 30 km/hr because you took 6 hrs to travel 180 km
We want to find your position when your average velocity is 30/3 = 10 km/hr
it took 3 hrs to go 90 km from A to B. Let t be the time lapsed since turn around
your displacement is given by d = 90 - 30(t)
and your total time of travel is t + 3 hrs
v = d/t
10 = (90 - 30t) / (t + 3)
10(t + 3) = (90 - 30t)
10t + 30 = 90 - 30t
40t = 60
t = 1.5 hrs
This will occur when you are halfway between B and A
By definition we have that the final speed is:
Vf² = Vo² + 2 * a * d
Where,
Vo: Final speed
a: acceleration
d: distance.
We cleared this expression the acceleration:
a = (Vf²-Vo²) / (2 * d)
Substituting the values:
a = ((0) ^ 2- (60) ^ 2) / ((2) * (123) * (1/5280))
a = -77268 mi / h ^ 2
its stopping distance on a roadway sloping downward at an angle of 17.0 ° is:
First you must make a free body diagram and see the acceleration of the car:
g = 32.2 feet / sec ^ 2
a = -77268 (mi / h ^ 2) * (5280/1) (feet / mi) * (1/3600) ^ 2 (h / s) ^ 2
a = -31.48 feet / sec ^ 2
A = a + g * sin (θ) = -31.48 + 32.2 * sin17.0
A = -22.07 feet / sec ^ 2
Clearing the braking distance:
Vf² = Vo² + 2 * a * d
d = (Vf²-Vo²) / (2 * a)
Substituting the values:
d = ((0) ^ 2- (60 * (5280/3600)) ^ 2) / (2 * (- 22.07))
d = 175.44 feet
answer:
its stopping distance on a roadway sloping downward at an angle of 17.0 ° is 175.44 feet
