A ball is thrown straight upward and then returns to the earth. choosing the positive direction to be upward, sketch a graph of the velocity of this ball against time. where does the velocity change direction? Explain?

doesn't it start to go downward at the top of the arc?

To sketch a graph of the velocity of the ball against time, we need to understand the motion of the ball.

When the ball is thrown upward, its velocity is initially positive because it moves in the positive direction (upward). As it continues to move upwards, the velocity decreases gradually until it reaches its highest point when the velocity is zero.

After reaching the highest point, the ball starts to move downward towards the earth. At this point, the direction of the velocity changes, and it becomes negative because the ball is moving in the opposite direction (downward). The velocity increases in magnitude until it reaches a maximum value, but with a negative sign.

When the ball reaches the ground, its velocity becomes zero again because it comes to rest momentarily before bouncing back up.

To summarize, the velocity is positive when the ball moves upward, decreases to zero at the highest point, becomes negative when the ball moves downward, reaches a maximum negative value, becomes zero again at the ground, and repeats the pattern.

Here's a rough sketch of the graph, showing the velocity of the ball against time:

v
| o
| o
| o
| o
| o
| o
---------------> t
Time

The change in velocity from positive to negative occurs at the highest point of the ball's trajectory. This happens because the ball experiences a change in its direction of motion from upward to downward. At this point, the velocity is zero, and then it starts to increase in the opposite direction.

To calculate the exact point where the velocity changes direction, we need additional information, such as the initial velocity of the ball and the time it takes for the ball to reach its highest point.