Consider a particle undergoing positive acceleration. (1) what is the shape of the position-time graph? (2) How do we determine an instantaneous velocity from the position-time graph?
if it is positive constant acceleration, distance is increasing with the square of time. Parabola shapped.
2. Vinst is the slope of the tangent to the position time curve.
When a particle undergoes positive acceleration, it means its velocity is increasing over time. To answer your questions:
1. The shape of the position-time graph:
The position-time graph shows the relationship between an object's position and time. In the case of positive acceleration, the graph will typically be a curve with a steeper slope as time progresses. The shape of the curve will depend on the specific acceleration profile, but it will have a concave-upward shape if the acceleration is constant.
2. Determining instantaneous velocity from the position-time graph:
To determine the instantaneous velocity from a position-time graph, you need to find the slope of the graph at a specific point. The slope of the position-time graph represents the rate of change of position with respect to time, which is the velocity.
To find the slope (instantaneous velocity) at a specific point on the graph, you can use calculus or approximations using smaller time intervals. Here's an approach using calculus:
- Identify the point on the position-time graph for which you want to find the instantaneous velocity.
- Find the derivative of the position-time graph with respect to time. This will give you the instantaneous velocity function.
- Evaluate the derivative at the desired point to find the specific instantaneous velocity.
Note: If the position-time graph is a curve with changing slope, the instantaneous velocity will also vary at different points along the curve.