Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation \frac{dV(t)}{dt}=-k(T-t);  where k> 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is

  • Option 1)

    I-\frac{k(T-t)^{2}}{2}\;

  • Option 2)

    \; \; e^{-kT}\;

  • Option 3)

    \; T^{2}-\frac{I}{k}\;

  • Option 4)

    \; I-\frac{kT^{2}}{2}

 

Answers (1)

As we learnt in 

Temperature Problems -

\frac{dT}{dt}= -k\left ( T-T_{m} \right )

- wherein

K is Proportionality constant

T = Temperature of body

T_{m}=  Temperature of Surrounding

 

 \int_{0}^{T}V(t)=\int_{0}^{T} -K(T-t)dt

V(t) -V(0)= -K(Tt-\frac{t^2}{2})|^T_0

V(t) -V(0)= -K(T^2-\frac{T^2}{2})

= \frac{-K.T^2}{2}

V(T )= V_0 -\frac{-K.T^2}{2}

V(T)= I-\frac{KT^2}{2}


Option 1)

I-\frac{k(T-t)^{2}}{2}\;

Incorrect

Option 2)

\; \; e^{-kT}\;

Incorrect

Option 3)

\; T^{2}-\frac{I}{k}\;

Incorrect

Option 4)

\; I-\frac{kT^{2}}{2}

Correct

Most Viewed Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 24999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions