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Last updated at April 19, 2021 by Teachoo

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Example 42 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 ๐ฅ=๐ก^2 (2โ๐ก/3). Find the time taken by it to reach Q and also find distance b/w P & Q Given Distance ๐ฅ = t2 (2โ๐ก/3) At points P and Q, the Velocity of the car is 0 Let ๐ฃ be the velocity of the car ๐ฃ = Change in Distance w.r.t ttime ๐ = ๐ ๐/๐ ๐ Finding ๐ ๐ฃ = ๐(๐ก^2 (2 โ ๐ก/3))/๐๐ก ๐ฃ = ๐(2๐ก^2โ ๐ก^3/3)/๐๐ก ๐ฃ = 4t โ t2 Putting ๐ = 0 4t โ t2 = 0 t(4โ๐ก)=0 So, t = 0 & t = 4 Thus, it takes 4 seconds to reach from point P to Q Also, Distance PQ = Distance travelled in 4 seconds Finding x at t = 4 ๐ฅ = t2 (2โ๐ก/3) ๐ฅ = (4)^2 (2โ4/3) = 16 ((6 โ 4)/3) = 16 (2/3) = 32/3 ๐. Hence, Distance PQ = ๐๐/๐ ๐.

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Chapter 6 Class 12 Application of Derivatives (Term 1)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.