Question

optional challenge question: this question is not worth any points. try it for fun if you get done early. a car has a mass of 1,000 kg. initially the car has a velocity of 15 m/s to the right. the car applies its brakes causing it to have some constant, negative acceleration to the left. it takes the car 200 meters to come to a complete stop. what must have been the braking force acting on the car? (assume the answer is in units of newtons, and dont forget to include a negative sign if your force points to the left)

Explanation:

Step1: Identify the kinematic - equation

We use the equation $v^{2}=v_{0}^{2}+2ax$, where $v = 0$ (final velocity, car stops), $v_{0}=15\ m/s$ (initial velocity), and $x = 200\ m$ (distance traveled).
$0=(15)^{2}+2a\times200$

Step2: Solve for acceleration $a$

First, expand the equation:
$0 = 225+400a$.
Then, isolate $a$:
$400a=- 225$, so $a=\frac{-225}{400}=-0.5625\ m/s^{2}$.

Step3: Use Newton's second - law

Newton's second - law is $F = ma$, where $m = 1000\ kg$ and $a=-0.5625\ m/s^{2}$.
$F=1000\times(-0.5625)$

Answer:

$- 562.5$