You throw a penny in the air with a velocity of 10 m/s [up]. The penny accelerates 10 m/s² [down]. How long?

Question

does it take to stop? Please help me!

Answer 1

1 second.

Answer 2

1 second. Because the penny is accelerating in the opposite direction of its motion, it is slowing down. 10 m/s^2 is the same as 10 m/s/s, which is to say, the penny slows down by 10 m/s every second. Since the penny only needs to slow down 10 m/s to get to zero, it will only take one second for it to slow down.

You can also used the equation: v = at + v0, you know:
v = 0 m/s (this is the final velocity)
a = -10 m/s^2 (this is negative because it's in the opposite direction)
v0 = 10 m/s (this is the initial velocity)
t = ? (this is what we're solving for)

Solve for t:
0 = at + v0 >> I replaced v with 0 because we know that, and it will make it simpler to solve for t
-v0 = at
t = -v0/a = -(10 m/s)/(-10 m/s^2) = 1 s

So this shows that it takes 1 second for the penny to slow from 10 m/s to 0 m/s at a constant downward acceleration of 10 m/s^2