You toss a coin straight up into the air. Sketch the velocity-time and acceleration-time graphs of the coin from the instant it leaves your hand until the instant it returns to your hand. Assume that the positive y direction is upward. Indicate on your graph the moment when the coin reaches its highest point.
To sketch the velocity-time and acceleration-time graphs of the coin, we first need to understand the motion of the coin as it moves upward and then downward.
When the coin is tossed straight up into the air, its initial velocity is positive in the upward direction. As it moves against the force of gravity, the velocity gradually decreases until it reaches a maximum height, where its velocity becomes zero. At this point, the coin starts moving downward with increasing velocity due to the gravitational force. Finally, the coin returns to your hand with a negative velocity.
Now, let's break down the coin's motion into two phases: upward and downward.
1. Upward Phase:
During the upward phase, the coin's velocity decreases while its acceleration is negative (opposite to the positive y direction). On the velocity-time graph, we will see a decreasing line that starts with a positive value and approaches zero at the highest point. The acceleration-time graph will have a constant negative value, indicating constant deceleration due to gravity during the upward motion.
2. Downward Phase:
During the downward phase, the coin's velocity increases while its acceleration remains constant but now in the positive y direction. On the velocity-time graph, we will see an increasing negative line, representing the coin's descending velocity. The acceleration-time graph will have a constant positive value, indicating constant acceleration due to gravity acting on the coin.
At the moment the coin reaches its highest point, the velocity is zero. Therefore, on the velocity-time graph, the point where the line crosses the horizontal axis (time-axis) represents the coin's highest point.
Remember, the coin's acceleration remains constant throughout its entire motion, both in the upward and downward phases.
Note: Since we don't have specific values for the velocity, acceleration, or time, we can only provide a qualitative representation of the graphs. The actual values will depend on the initial velocity and the height to which the coin is thrown.