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| Velocity-Time Graph |
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| The variation of velocity with time can be represented graphically to calculate acceleration exactly like we calculated speed from distance-time graph. |
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| Let us now plot a velocity-time (v- t)
graph for the following data. |
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| Velocity
- time graph |
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 Take time along x-axis and velocity along y-axis. |
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 Analyze the given data and make a proper choice of scale for x and y axes. |
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 Plot the given points. |
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 Consider any two points A and B on the straight-line graph. |
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 Draw perpendiculars from A and B to x and y-axes. |
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 Join A to C, ACB forms a right-angled triangle. |
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| Calculations |
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 Write the title and scale chosen for the graph. |
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| Let us now see the nature of the v - t graph for the different types of motion. |
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| Nature of
v-t graph |
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| The following results can be deduced from velocity-time graph. |
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 The acceleration produced in a body |
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 The distance covered by a moving object |
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 We can derive the equations of motion |
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| Let us see how to calculate the distance covered by a moving object from speed-time graph. |
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| The figure below gives the speed-time graph of a car moving with a uniform speed of 60kmp/hr for 5 hours. |
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| Speed-Time graph of a car moving with a uniform speed |
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| Distance traveled by the car (s) = v x t |
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| But 60 km/h = BC = breadth of the rectangle OABC |
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| 5hr = OC = length of the rectangle OABC |
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| i.e., the distance covered by the car = length x breadth = 300 km. |
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| i.e., in order to calculate the distance covered by a moving object from a speed-time graph we just have to find the area enclosed by the speed-time graph and the time axis. |
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| In case of non-uniform motion, the distance covered by the object cannot be found as the product of speed and time interval given by the speed-time graph because the speed does not remain constant throughout its motion. But, it is given by the area enclosed by the speed-time graph and the time axis. |
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| The figure given below gives the motion
of an object moving with variable speed. |
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| Motion of an object moving with variable speed |
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| The speed of the object is increasing in steps. The speed remains constant during the time interval 0 - t1, t1 - t2, t2 - t3 ...... |
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 The total distance covered by the object during the time interval |
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| 0 ----> t6 = Area of rectangle 1 + area of rectangle 2 +……+ area of rectangle 6. |
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