A ball rolls across a floor with an acceleration of 0.100 m/s2 in a direction opposite to its velocity.The ball has a speed of 4.00 m/s after rolling a distance 6.00 m across the floor.What was the initial speed of the ball?Express your answer in m/s.
Question
A ball rolls across a floor with an acceleration of 0.100 m/s2 in a direction opposite to its velocity.The ball has a speed of 4.00 m/s after rolling a distance 6.00 m across the floor.What was the initial speed of the ball?Express your answer in m/s.
Solution
To solve this problem, we can use the equation of motion that relates final velocity (v), initial velocity (u), acceleration (a), and distance (s). The equation is:
v^2 = u^2 + 2as
Given in the problem, we have:
v = 4.00 m/s (final speed) a = -0.100 m/s^2 (acceleration, it's negative because it's in the opposite direction of the velocity) s = 6.00 m (distance)
We can plug these values into the equation and solve for u (initial speed):
(4.00 m/s)^2 = u^2 + 2*(-0.100 m/s^2)*(6.00 m)
16.00 m^2/s^2 = u^2 - 1.20 m^2/s^2
Adding 1.20 m^2/s^2 to both sides gives:
17.20 m^2/s^2 = u^2
Taking the square root of both sides gives the initial speed:
u = sqrt(17.20 m^2/s^2) = 4.15 m/s
So, the initial speed of the ball was 4.15 m/s.
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