The position time-graph for the motion of a certain particle is a smooth curve, like a parabola.At a given instant of time the tangent line to t he position-time graph has a negative slope. is the instantaneous velocity of the particle at this time positive, negative, or zero?Explain
positive
1) can the position-time graph for the motion of an object be a horizontal line?explain
-yes
2) can the positon-time graph bea vertical line, explain
-no
velocity = change in position/change in time = slope of position time graph.
If the slope is negative, the velocity is negative
why not? constant y, going right or left
why not? constant x, going up or down
1) can the position-time graph for the motion of an object be a horizontal line?explain
- so its yes?
2) can the positon-time graph bea vertical line, explain
-so its yes
To determine the instantaneous velocity of a particle at a given time when the tangent line to the position-time graph has a negative slope, we need to understand the relationship between the slope of the tangent line and the velocity.
In a position-time graph, the slope of the tangent line at any point represents the velocity of the particle at that particular instant. The slope indicates how position changes with respect to time. If the slope is positive, the velocity is positive, indicating motion in the positive direction. If the slope is negative, the velocity is negative, indicating motion in the negative direction. If the slope is zero, the velocity is zero, indicating no motion.
In this scenario, since the tangent line has a negative slope, it means the particle's position is decreasing with respect to time. Therefore, the instantaneous velocity of the particle at this specific time is negative. This suggests that the particle is moving in the negative direction at this instant.