Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12



  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise


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 ๐‘ฅ=๐‘ก^2 (2โˆ’๐‘ก/3). Find the time taken by it to reach Q and also find distance b/w P & Q Given distance ๐‘ฅ = t2 (2โˆ’๐‘ก/3) Let v be the velocity of the car at t second ๐‘ฃ = change in distance w.r.t t i.e. ๐‘ฃ = ๐‘‘๐‘ฅ/๐‘‘๐‘ก ๐‘ฃ = ๐‘‘(๐‘ก^2 (2 โˆ’ ๐‘ก/3))/๐‘‘๐‘ก ๐‘ฃ = ๐‘‘(2๐‘ก^2โˆ’ ๐‘ก^3/3)/๐‘‘๐‘ก ๐‘ฃ = 4t โ€“ t2 Putting v = 0 โ‡’ 4t โ€“ t2 = 0 โ‡’ t(4โˆ’๐‘ก)=0 So, t = 0 & t = 4 Hence, the car is not moving at t = 0 & t = 4 second Now, car is not moving (i.e. v = 0) at point P as well as at point Q Thus the car will reach the point Q after 4 seconds โ‡’ Distance PQ = Distance travelled in 4 seconds Finding x at t = 4 ๐‘ฅ = t2 (2โˆ’๐‘ก/3) ๐‘ฅ = (4)^2 (2โˆ’4/3) = 16 ((6 โˆ’ 4)/3) = 16 (2/3) = 32/3 ๐‘š. Hence, Distance PQ = ๐Ÿ‘๐Ÿ/๐Ÿ‘ ๐’Ž.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.