A car starts from a point P at time t = 0 seconds and stops at point Q. The distance x, in metres, covered by it, in t seconds is given by `x=t^2(2-t/3)`Find the time taken by it to reach Q and also find distance between P and Q.

Explanation

`x=t^{2}(2-frac{t}{3})=2 t^{2}-frac{t^{2}}{3}`
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therefore frac{d x}{d t}=4 t-t^{2}=t(4-t)`
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therefore V=t(4-t)`

Now, ` v=0 Rightarrow t(4-t)=0 Rightarrow Now t=0 `is the time at starting point P
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therefore t=4 `seconds is the time to recover distance P Q .

P Q=d i s t a n c e covered in 4 seconds
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=(4)^{2}[2-frac{4}{3}]=16(frac{2}{3})=frac{32}{3}`
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therefore P Q=frac{32}{3} metres.`