The distance-time graph of a moving vehicle is as shown in...

The distance-time graph of a moving vehicle is as shown in the figure.
(1) The speed of the vehicle is increasing with time.
(2) The speed of the vehicle is decreasing with time.
(3) The final speed of the vehicle is zero.
(4) Graph is not possible.

Key Concepts

Distance-Time Graph

A distance-time graph is a graphical representation that shows how far an object has traveled over a period of time. It is a fundamental tool in kinematics that helps visualize the motion of an object, where the distance is plotted along the vertical axis and time along the horizontal axis.

Slope and Speed

The slope of a distance-time graph represents the speed of the moving object. A steeper slope indicates a higher speed, and the rate of change of the distance with respect to time shows whether the object is moving quickly or slowly. If the slope increases, the speed is increasing; if it decreases, the speed is decreasing.

Instantaneous vs. Average Speed

Instantaneous speed is determined by finding the slope (derivative) at a specific point on the distance-time graph, while average speed is calculated over a longer interval by dividing the total distance by the total time. This concept is key when analyzing changes in speed over time based on the graph.

Physical Feasibility of Motion Graphs

In kinematics, a graph must represent a physically realistic scenario. Analyzing whether a graph is possible involves checking if the changes in slope (and thus speed and acceleration) are consistent with the laws of motion. This includes ensuring that transitions in speed are smooth and continuous unless otherwise justified by an instantaneous change.

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