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

Last updated date: 29th May 2024
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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.