Physics | Vertical Projectile Motion | Graphs

The video begins with an introduction to projectile motion graphs, emphasizing their importance for various exams. The instructor encourages viewers to subscribe to the channel for more lessons and to engage by liking the video. The focus then shifts to the first type of graph to be discussed: the velocity-time graph. The instructor sets up the context by describing a scenario of dropping an object from a building, explaining that the velocity will increase until impact and starts at an initial velocity of zero. The importance of labeling the graph is highlighted, with velocity on the y-axis and time on the x-axis. The instructor then explains that the graph for this scenario would be a straight line with a positive slope, indicating increasing velocity over time.

This paragraph delves deeper into the specifics of velocity-time graphs for different scenarios. The instructor first discusses the case of an object being dropped, noting that the graph would start at zero velocity and increase linearly due to the constant acceleration of gravity. The direction of positive velocity is chosen to be downwards, resulting in a positive slope. The instructor also explains the implications of choosing 'up' as the positive direction, which would result in a negative slope. The paragraph continues with a scenario of throwing a ball vertically upwards, where the velocity starts positive, decreases to zero at the peak, and then becomes negative as the ball falls back down. The instructor illustrates how the graph would reflect this motion, with a line that starts positive, crosses the time axis at the peak, and then continues negatively.

The instructor explains the connection between the velocity-time graph and displacement. By analyzing the area under the velocity-time graph, the viewer can determine the displacement of the object. The area under the graph is calculated as half the base (time) multiplied by the height (velocity), resulting in units of meters, which represent displacement. The instructor uses a triangle to illustrate this concept, showing that the area under the graph before the object reaches its maximum height and after it falls back down can be used to calculate the total displacement. The paragraph reinforces the idea that the gradient under the velocity-time graph represents gravitational acceleration, which is constant at 9.8 m/s².

The discussion moves to position-time graphs, starting with a scenario where an object is thrown upwards and then falls back to the ground. The instructor uses the ground as a reference point, with the graph beginning at a positive position if the object is thrown from a height. As time progresses, the object's position decreases towards the ground, resulting in a downward-sloping line on the graph. If the direction 'up' is considered positive, the graph will start above the time axis and move downwards, indicating the object's decreasing height. The instructor also mentions that if 'down' is considered positive, the graph would reflect this by starting below the time axis and moving upwards, which would complicate the visualization.

The instructor introduces acceleration-time graphs, noting that acceleration due to gravity remains constant at 9.8 m/s², regardless of the object's motion. The graph for gravitational acceleration is a straight horizontal line at -9.8 m/s² if 'up' is considered positive, or +9.8 m/s² if 'down' is positive. The paragraph then transitions to a bouncing ball scenario, where the ball is thrown upwards, misses a catch, bounces off the ground, and reaches a new height before coming to rest. The instructor labels different points of the ball's trajectory and begins to draw the relevant velocity-time graph, indicating how the velocity changes from positive to negative and back to positive as the ball bounces.

This paragraph focuses on the specifics of the velocity-time graph for a bouncing ball that undergoes an inelastic collision with the ground. The instructor explains that the velocity of the ball just before it touches the ground would be high and positive, but upon impact, some energy is converted into other forms, resulting in a lower velocity as the ball leaves the ground. The graph would show a sudden change in direction from negative to positive at the moment of impact, reflecting the change in velocity due to the collision. The instructor uses approximate values to illustrate the concept and emphasizes the brief period of time over which this change occurs.

The instructor describes the position-time graph for the bouncing ball scenario. Starting from a height, the ball's position is plotted against time, resulting in a parabolic shape. The graph begins at the initial height, rises to the first maximum height (the apex of the ball's trajectory), then turns and descends until it reaches the ground. There is a brief time lapse at the point of impact with the ground, after which the ball ascends again to a lower maximum height, following the parabolic curve. The instructor notes that the shape of the graph remains the same regardless of whether the ground or the point of throw is considered the zero position.

The acceleration-time graph for the bouncing ball scenario is discussed, with the instructor pointing out that the graph would show a constant gravitational acceleration of -9.8 m/s², as acceleration due to gravity is constant and acts downwards. However, at the moment of impact with the ground, the ball experiences an extremely large upward force, resulting in a brief period of positive acceleration. This is represented by an almost vertical line on the graph, indicating a very high acceleration for a short time as the ball changes direction. After leaving the ground, the acceleration returns to -9.8 m/s², continuing as a constant value.

In the concluding paragraph, the instructor summarizes the key points covered in the video, including the velocity-time and position-time graphs for various scenarios such as free fall, vertical throws, and bouncing balls. The instructor expresses hope that the video has been helpful and encourages viewers to like the video and subscribe to the channel for more physics lessons. There is a mention of future plans to work through past exam questions to demonstrate the application of these concepts and to interpret graphs for answering related questions.