Example 42 - A car starts from a point P at time t = 0 seconds

Example 42 - Chapter 6 Class 12 Application of Derivatives - Part 2
Example 42 - Chapter 6 Class 12 Application of Derivatives - Part 3

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

Transcript

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 π‘₯=𝑑^2 (2βˆ’π‘‘/3). Find the time taken by it to reach Q and also find distance b/w P & Q Given Distance π‘₯ = t2 (2βˆ’π‘‘/3) At points P and Q, the Velocity of the car is 0 Let 𝑣 be the velocity of the car 𝑣 = Change in Distance w.r.t ttime 𝒗 = 𝒅𝒙/𝒅𝒕 Finding 𝒗 𝑣 = 𝑑(𝑑^2 (2 βˆ’ 𝑑/3))/𝑑𝑑 𝑣 = 𝑑(2𝑑^2βˆ’ 𝑑^3/3)/𝑑𝑑 𝑣 = 4t – t2 Putting 𝒗 = 0 4t – t2 = 0 t(4βˆ’π‘‘)=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 π‘₯ = t2 (2βˆ’π‘‘/3) π‘₯ = (4)^2 (2βˆ’4/3) = 16 ((6 βˆ’ 4)/3) = 16 (2/3) = 32/3 π‘š. Hence, Distance PQ = πŸ‘πŸ/πŸ‘ π’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 10 years. He provides courses for Maths and Science at Teachoo.