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The slope of a distance time graph is a measure of the rate of change in the distance of the object from a fixed reference point along the radial direction. If there were no acceleration in that direction then the radial velocity would be the same so that the graph would be a straight line. However, a curve indicates not only the the distance is changing with time, but that the rate of change is also changing. That is, the radial velocity is changing and that is indicative of radial acceleration.
The word "radial" appear many times in the above paragraph. This is to emphasise that distance time graphs look only at the motion of an object in the direction towards or away from the reference point. Any motion is a transverse direction is ignored. Thus, a line with a constant gradient (slope) does not indicate that there is no acceleration but that any acceleration is in the direction at right angles to the reference direction.
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ProfessorA curve on a distance-time graph indicates acceleration because the slope of the curve represents the speed of the object at different points in time. If the slope of the curve is increasing, it means the object is accelerating because it is covering more distance in less time, hence speeding up.
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What does the slope of a tangent to the curve of a velocity-time graph measure?
The slope of a tangent to the curve of a velocity-time graph represents the acceleration of an object at that specific instant in time. A steeper slope indicates a greater acceleration, while a flatter slope indicates a smaller acceleration.
On a velocity vs time graph shows what about an objects motion?
A velocity vs. time graph shows how the velocity of an object changes with respect to time. The slope of the graph represents the object's acceleration, while the area under the curve represents the distance traveled by the object. Flat sections of the graph indicate constant velocity, while curved sections show changes in acceleration.
What does a negative acceleration position-time graph indicate about the motion of an object?
A negative acceleration position-time graph indicates that the object is slowing down or decelerating.
What does the slope of the tangent to the curve on a velocity-time graph measure?
The slope of the tangent to the curve on a velocity-time graph represents the acceleration of an object. Positive slope indicates acceleration in the positive direction, negative slope indicates acceleration in the negative direction, and zero slope indicates constant velocity.
How Would The Acceleration vs Time Graph Look?
The acceleration vs. time graph would show how an object's acceleration changes over time. A horizontal line at zero acceleration would indicate constant velocity. A straight line with a positive or negative slope would represent constant acceleration. A curved line would indicate changing acceleration.
