"\\text a(t)=\\text v'(t)={A \\over t_{max\\_ speed}}e^{-{t \\over t_{max\\_speed}}}""\\text v(t)=A(1-e^{-{t \\over t_{max\\_ speed}}})"
"\\text s(t)=\\int \\text v(t) dt=\\int A(1-e^{-{t \\over t_{max\\_ speed}}})dt="
"=A(t+t_{max\\_speed}\\cdot e^{-{t \\over t_{max\\_ speed}}})+C"
"\\text s(0)=0=>C=-A\\cdot t_{max\\_speed}"
"\\text s(t)=A(t-t_{max\\_speed}+t_{max\\_speed}\\cdot e^{-{t \\over t_{max\\_ speed}}})"
Given that
"\\text v(2.6)=A(1-e^{-{2.6 \\over t_{max\\_ speed}}})=28"
"\\text s(10.46)=""A(10.46-t_{max\\_speed}+t_{max\\_speed}\\cdot e^{-{10.46 \\over t_{max\\_ speed}}})=400"
"t_{max\\_speed}\\approx5.834\\ s" or "t_{max\\_speed}\\approx28.424 \\ s"
"A\\approx77.864\\ m\/s" or "A\\approx320.318\\ m\/s"
"t_{max\\_speed}\\approx5.834\\ s,A\\approx77.864\\ m\/s"
"\\text a_{max}={77.864\\ m\/s\\cdot e^{-1} \\over 5.834\\ s}\\approx4.910\\ m\/s^2"
Or
"t_{max\\_speed}\\approx28.424\\ s,A\\approx320.318\\ m\/s"
"\\text a_{max}={320.318\\ m\/s\\cdot e^{-1} \\over 28.424\\ s}\\approx4.146\\ m\/s^2"
"202.480\\ m\/s\\approx729\\ km\/h"
I think, that the car cannot have such speed.
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