Answer:
20 m
Explanation:
There are two methods we can use to find the distance traveled. One method is the work-energy theorem, which says the work done by the stopping force is equal to the car's change in kinetic energy. Another method is to use Newton's second law of motion to find the acceleration, then use a kinematic equation to solve for the distance.
Using the work energy theorem, work (W) is equal to the change in kinetic energy (KE). Work is equal to force (F) times distance (d), and kinetic energy is half the mass (m) times the square of the speed (v).
W = ΔKE
Fd = ½ mv²
(2500 N) d = ½ (1000 kg) (10 m/s)²
d = 20 m
Alternatively, using Newton's second law of motion, the net force (F) is equal to the mass (m) times the acceleration (a).
F = ma
-2500 N = (1000 kg) a
a = -2.5 m/s²
Use a kinematic equation, also known as a SUVAT equation.
v² = u² + 2as
(0 m/s)² = (10 m/s)² + 2 (-2.5 m/s²) d
d = 20 m
