Answer:
Yes, it will reach the gas station.
Explanation:
The kinetic energy of an object is equal to half its mass times the square of its speed. Given the kinetic energy and mass, the initial speed of the car can be found. Afterward, two methods can be used to find the distance traveled by the car while decelerating. Method 1: the work-energy theorem says that the work done is equal to the change in kinetic energy. Method 2: Newton's second law of motion says that the net force on the car is equal to its mass times acceleration; the distance traveled can then be found with kinematics.
Initial speed
First, use the kinetic energy to find the initial speed.
KE = ½ mv²
where m is mass and v is speed.
Given:
KE = 10,000 kJ = 10,000,000 J
m = 8500 kg
Find: v
10,000,000 J = ½ (8500 kg) v²
v = 48.5 m/s
Method 1: Work-energy
The distance the car travels can be found with work-energy theorem.
W = ΔKE
W = KE − KE₀
The car comes to a stop, so its final kinetic energy is zero. The work done by friction is equal to the force times the distance.
Fd = 0 − KE₀
(-5000 N) d = -10,000,000 J
d = 2000 m
Method 2: Force and kinematics
The distance traveled can also be found using Newton's second law and kinematics.
F = ma
-5000 N = (8500 kg) a
a = -0.588 m/s²
v² = u² + 2as
(0 m/s)² = (48.5 m/s)² + 2 (-0.588 m/s²) s
s = 2000 m
Answer
The car travels 2000 meters, or 2 km. It will easily be able to reach the gas station.
