Using Position–Time Graph to Calculate Average Velocity: Jet Car, Take Two

Calculate the instantaneous velocity of the jet car at a time of 25 s by finding the slope of the tangent line at point Q in Figure 2.13.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point.
2
Solution
1. Find the tangent line to the curve at $t = 25 s$ .
2. Determine the endpoints of the tangent. These correspond to a position of 1,300 m at time 19 s and a position of 3120 m at time 32 s.
3. Plug these endpoints into the equation to solve for the slope, v.
  $\begin{matrix} slope & = & v_{Q} = \frac{Δ d_{Q}}{Δ t_{Q}} \\ = & \frac{(3120 - 1300) m}{(32 - 19) s} \\ = & \frac{1820 m}{13 s} \\ = & 140 m/s \end{matrix}$
  2.9

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