Calculating Acceleration from a Graph of Velocity versus Time

Calculate the acceleration of the jet car at a time of 25 s by finding the slope of the $v$ vs. $t$ graph in Figure 2.51(a).

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Strategy
The slope of the curve at $t = 25 s$ is equal to the slope of the line tangent at that point, as illustrated in Figure 2.51(a).
Solution
Determine endpoints of the tangent line from the figure, and then plug them into the equation to solve for slope, $a$ .
$slope = \frac{Δ v}{Δ t} = \frac{(260 m/s - 210 m/s)}{(51 s - 1.0 s)}$
2.100

$a = \frac{50 m/s}{50 s} = 1 . 0 m {/s}^{2} .$
2.101
Discussion
Note that this value for $a$ is consistent with the value plotted in Figure 2.51(b) at $t = 25 s$ .

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