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Question
How does the slope of a speed-time graph give the acceleration of a body moving along a straight line?
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Solution
Slope of a graph is given as rate of change of y coordinates to the x coordinate. In speed time graph speed is on the y axis and time is on the x axis. And we define acceleration as rate of change of speed with respect to time. So slope of a speed time graph gives acceleration.
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(i) In speed time graph uniform motion is given by a straight line parallel to x axis so figure (a) denotes the uniform motion.
(ii) In speed time graph motion with increasing speed is shown by straight line with positive slope so figure (c) denotes the motion with speed increasing.
(iii) In speed time graph motion with decreasing speed is shown by straight line with negative slope so figure (b) denotes the motion with speed decreasing.
(iv) In speed time graph motion with oscillating speed is shown by zigzag line so figure {d) denotes the motion with speed oscillating.
