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mash [69]
3 years ago
8

10

Mathematics
1 answer:
Anestetic [448]3 years ago
8 0

Answer:

Acceleration when time is 2 \ sec = -\frac{5}{4} \ m/s^2

Distance s=9-\frac{9}{t}

Distance travelled between t=1 and t=3 is 6\ m

Step-by-step explanation:

Velocity V=1+\frac{9}{t^2} \ \ \ when \ \ 1\leq t\leq 3

<u><em>Acceleration(a):</em></u><u><em> Rate of change of velocity.</em></u>

a=\frac{dV}{dt} =1-\frac{18}{t^3}

at t=2

a=1-\frac{18}{8} \\=1-\frac{9}{4} \\=-\frac{5}{4}

a=-\frac{5}{4} \ m/s^2

<u><em>Distance(s):</em></u>

V=\frac{ds}{dt}\\\\\frac{ds}{dt}=1+\frac{9}{t^2}\\\\Integrate\ both\ sides\\\\s=1-\frac{9}{t}+k\\\\ k\ is\ a\ constant\\\\Given\ s=6\ when\ t=3\\\\6=1-\frac{9}{3}+k\\\\ k=8\\\\Hence\ s=1-\frac{9}{t}+8\\\\ s=9-\frac{9}{t}

<u><em>Distance between t=1 \ and \ t=3</em></u>

=s(3)-s(1)\\\\=(9-\frac{9}{3})-(9-9) \\\\=6 \ m

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