I want to double check that my solutions are correct:
- An elevator is traveling upward at 10 m/s. It slows to a stop at the designated floor in 4 s. What is the acceleration of the elevator while it is stopping?
$v=at+v_0$
$0 m/s = a(4s)+10m/s$
$a=\frac{-10}{4}m/s^2$
- A roller coaster is coasting over a flat piece of track at 100 km/hr. It proceeds down a hill that causes an acceleration of 0.4 m/s^2 for 5 seconds. What will the speed be at the end of the hill?
$v=at+v_0$
$100km/hr \approx 27.7 m/s$
$v=(0.4m/s^2)(5s)+(27.7m/s)$
$v=29.7 m/s$
- A car traveling down the highway at 38 m/s notices a cop parked on the side of the road. In an effort to avoid a ticket, they slam on the brakes, causing an acceleration of -2 m/s^2. How much time will they need to slow down to the legal limit of 27 m/s?
$v=at+v_0$
$27m/s=(-2m/s^2)t+38m/s$
$-11m/s=(-2m/s^2)t$
$t=\frac{-11}{-2}s=5.5s$