Hello, In my class, we are on the anti-derivative unit now....so I am sure this

Question

Hello,

In my class, we are on the anti-derivative unit now....so I am sure this question has something to do with it. I keep getting the wrong answer for displacement, and I don;t know what the answer is. So I need help! I might be attacking this the wrong wat.

One night a mosquito is looking for some blood and its velocity is given by v(t) = 0.8t^2 cm/s after t seconds moving in straight line. It flies past a campfire and through a hole in a tent where its s = 10m from campfire and when t = 0 seconds.

a) FIND THE DISPLACEMENT FROM CAMPFIRE WHEN T = 7 SECONDS

Explanation / Answer

a)

given velocity = 0.8 t^2 cm / sec = 0.8 * 10-2 * t^2 = 0.008t^2 m/sec

now velocity = ds / dt

where s = displacement

so ds/dt = 0.008 t^2

so ds = 0.008 t^2 dt

integrating

s = 0.008/3 * t^3 + c

where c is an integration constant

given .. at t = 0 ,, s = 10 m

so puttinf these values in the equation

10 = 0 + c

so we get c = 10

the equation now becomes

displacement s = (0.008/3)*t^3 + 10

so for t = 7 sec

s = (0.008/3)*7^3 + 10 = 10.91467 metres

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