Home
Class 12
MATHS
If F is the constant force generated by ...

If F is the constant force generated by the motor of an automobiles of mass M, its velocity V is given by `M(dV)/(dt)=F-kV`, where k is a constant. Express V in terms of t given that V = 0 when t = 0.

Text Solution

Verified by Experts

The correct Answer is:
`F = (F-kV)e^((kt)/M)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ORDINARY DIFFERENTIAL EQUATIONS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 10.6|8 Videos

  • ORDINARY DIFFERENTIAL EQUATIONS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 10.7|15 Videos

  • ORDINARY DIFFERENTIAL EQUATIONS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 10.4|10 Videos

  • MODEL QUESTION PAPER -1

    PREMIERS PUBLISHERS|Exercise Part -IV|20 Videos

  • PROBABILITY DISTRIBUTIONS

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|40 Videos

Similar Questions

Explore conceptually related problems

If F is the constant force generated by the motor of an automobile of mass M , its velocity V is given by M(dV)/(dt)=F-kV , where k is a constant. Express V in terms of t given that V=0 when t = 0.

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 (d V(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 : (1) T^2-1/k (2) I-(k T^2)/2 (3) I-(k(T-t)^2)/2 (4) e^(-k T)

Knowledge Check

  • If V_(0) is the stopping potential of an electron of mass 'm' charge 'e' and its mass velocity is given by

    A
    `( meV_(0))/(2)`
    B
    `sqrt((meV_(0))/(2))`
    C
    `sqrt((2eV_(0))/(m)0`
    D
    `(2eV_(0))/(m)`

  • The equation of SHM of a particle is (d^(2)y)/(dt^(2))+ky=0 , where k is a positive constant. The time period of motion is given by……………..

    A
    `(2pi)/(sqrt(k))`
    B
    `(2pi)/(k)`
    C
    `(k)/(2pi)`
    D
    `(sqrt(k))/(2pi)`

  • The frequency of vibration v of mass m suspended from a spring of spring constant k is given by f=cm^(x)k^(y) where c is a dimensional constant. The volumes of x and y are :

    A
    `x=(1)/(2), y=(1)/(2)`
    B
    `x=(1)/(2), y=-(1)/(2)`
    C
    `x=-(1)/(2), y=(1)/(2)`
    D
    `x=-(1)/(2), y=-(1)/(2)`

    • Similar Questions

    Explore conceptually related problems

    According to Einstein’s theory of relativity, the mass m of a body moving with velocity v is m = (m_(0))/(sqrt(1-(v^(2))/(c^(2)))) , where m_(0) is the initial mass and c is the speed of light. What happens to m as v rarr c^(-) . Why is a left hand limit necessary?

    A particle moves in a circle of radius 20 cm. Its linear speed is given by v=2t, where t is in second and v in metre/ second. Find the radial and tangential acceleration at t=3s.

    The Fahrenheit remperature F and absolute temperature K satisfy a linear equation. Given that K = 273 " when " F = 32 and that K = 373 when F = 212. Express K in terms of F and find the value of F, when K = 0 .

    The force of resistance encountered by water on a motor boat of mass m going in still water with velocity v is proportional to the velocity vdot At t=0 when its velocity is v_0, then engine shuts off. Find an expression for the position of motor boat at time t and also the distance travelled by the boat before it comes to rest. Take the proportionality constant as k > 0.

    A particle of mass m is moving in a horizontal circle of radius r under centripetal force given by (- k//r^(2)) where k is a constant . Then the total energy of the particle is _________ .

    Home
    Profile