A ball rolling across a field with an acceleration of -0.5 m/s rolls 12.5 m and then comes to a stop after 8 seconds.
What was the ball's initial speed?
deceleration rate * time = Initial speed
= 4 m/s.
It should come to rest after rolling a distance (average speed)*(time) = 16 meters.
You have been given more infrmation that you need, and some of it is inconsistent.
Your deceleration rate also has the wrong units. m/s is not correct units for acceleration
Well, it seems like this ball was really taking its time! It rolled a whole 12.5 meters in 8 seconds before finally coming to a stop. I gotta say, that's some dedication to laziness!
Now, to find the initial speed of the ball, we can use the equation:
v = u + at
Where:
v is the final velocity (which is 0 m/s, since the ball came to a stop),
u is the initial velocity (what we're trying to find),
a is the acceleration (-0.5 m/s², since it was slowing down), and
t is the time (8 seconds).
Plugging in the values, we get:
0 = u + (-0.5 m/s²)(8 s)
Simplifying, we find:
0 = u - 4 m/s
To make the equation a little more helpful, we can rearrange it:
u = 4 m/s
And there you have it! The ball's initial speed was 4 meters per second. So, even though it took its sweet time, it started off with a bit of a kick!
To solve this problem, we can use the equation of motion:
vf = vi + at
Where:
vf = final velocity (0 m/s, since the ball comes to a stop)
vi = initial velocity (what we're trying to find)
a = acceleration (-0.5 m/s^2)
t = time (8 seconds)
Rearranging the equation, we have:
vi = vf - at
Substituting the given values, we get:
vi = 0 - (-0.5 m/s^2 * 8 s)
Simplifying the equation, we have:
vi = 0 + 4 m/s
Therefore, the ball's initial speed was 4 m/s.
To find the ball's initial speed, we can use the equation of motion:
v = u + at
Where:
v = final velocity (0 m/s since the ball comes to a stop)
u = initial velocity (unknown)
a = acceleration (-0.5 m/s²)
t = time (8 s)
Rearranging the equation, we have:
u = v - at
Substituting the values, we get:
u = 0 - (-0.5 m/s² * 8 s)
u = 4 m/s
Therefore, the ball's initial speed was 4 m/s.