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Which car has the highest speed and which car has the lowest speed?


seo-qna
Last updated date: 29th May 2024
Total views: 47.4k
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Answer
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Hint: Recall the various graphs in kinematics and what the properties of the graphs are. Also recall what area under the curve and slope of each graph gives. Answer accordingly to the data given in graphs.

Formula used:
Slope $ = \dfrac{{\Delta y}}{{\Delta x}} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$

Complete step by step solution:
The given graph is a $x - t$ graph. We know that the slope of $x - t$ graph gives the speed. Thus the car whose slope is maximum has the maximum speed. Hence for these we need to find the slope in each case. We know,
Slope $ = \dfrac{{\Delta y}}{{\Delta x}} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
Thus,
Slope of A $ = \dfrac{{14 - 6}}{{1.6 - 0}} = \dfrac{8}{{1.6}} = 5km/hr$
Slope of B $ = \dfrac{{14 - 0}}{{1.4 - 0}} = \dfrac{{14}}{{1.4}} = 10km/hr$
Slope of C $ = \dfrac{{14 - 2}}{{1.0 - 0}} = \dfrac{{12}}{{1.0}} = 12km/hr$

After taking out the slopes, we infer that C has the maximum slope and A has the minimum slope.

Thus, C has the maximum speed and A has the minimum speed.

Additional Information:
There are three main motion graphs that tend to be studied in kinematics: displacement-time graphs, velocity-time graphs, and acceleration-time graphs. In all the three, time is present in the X-axis, while the others are present in Y-axis.
Following shows what does the slope and area of each graph corresponds to
GraphSlopeArea
Displacement-timeVelocity---
Velocity-timeAccelerationDisplacement
Acceleration-time---Velocity

Graphs are an easy way to study the nature of motion of a body. A curve in any of the graphs may not be a straight line; it can even be a curve.

Note: Do the calculations properly. Also do not make mistakes in interpreting the graph. Keep in mind the properties of all the graphs in kinematics within the scope of syllabus.