Randall D. Knight — Kinematics in One Dimension: Problem Problem_69

If a Tesla Model S P100D in “Ludicrous mode” is pushed to its limit, the first 3.0 s of acceleration can be modeled as \[ a_x = \begin{cases} (35 \text{ m/s}^3)t & 0 \text{ s} \leq t \leq 0.40 \text{ s} \\ 14.6 \text{ m/s}^2 - (1.5 \text{ m/s}^3)t & 0.40 \text{ s} \leq t \leq 3.0 \text{ s} \end{cases} \] a. How long does it take to accelerate to 60 mph? Your answer, which seems impossibly short, is confirmed by track tests. b. What acceleration would be needed to achieve the same speed in the same time at constant acceleration? Give your answer as a multiple of \( g \).