When I toss a ball straight up, it travels up, stops, and then falls back to by hand. When it stops to change direction, how long is it stopped?
The veloicty is linear
As an example
V=10- 10t so at t=1, velocity is zero. Is it zero at .999999999999 or 1.0000000001 sec? No.
What does that tell me? Just as a point in space has no dimension while a line does, is there a period of time that has no "length",ie ifinantely short?
To determine how long the ball is stopped when it changes direction, we can use the laws of motion.
When you toss a ball straight up, it experiences a constant acceleration due to gravity pulling it downward. At the highest point of its trajectory, the velocity becomes zero, and it starts to fall back down.
To find the time the ball is stopped, we can use the equation of motion:
velocity = initial velocity + (acceleration * time).
Since the initial velocity when the ball is thrown straight up is known (let's assume as "v"), and the acceleration due to gravity is a constant value (-9.8 m/s² near the surface of the Earth), we can use those values to find the time it takes to reach the highest point.
At the highest point, the velocity is zero. So, we can set the equation to zero and solve for time:
0 = v - (9.8 * t)
Rearranging the equation:
v = 9.8 * t
Solving for time (t):
t = v / 9.8
This gives us the time it takes for the ball to reach its highest point. To find the total time the ball is stopped, we can double this value since the falling phase has the same duration as the ascent:
Total time stopped = 2 * (v / 9.8)
Note that the value of "v" depends on how fast you toss the ball initially.