Home
Class 11
MATHS
The distance travelled by a particle up...

The distance travelled by a particle upto tiem x is given by `f(x)=x^(3)-2x+1.` The time c at which at velocity of the particle is equal to its average velocity between times x=-1 and x=2 sec. is

A

15 sec

B

`sqrt((3)/(2))` sec

C

`sqrt(3)` sec

D

`sqrt((7)/(3))` sec

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|4 Videos
  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos
  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

Similar Questions

Explore conceptually related problems

The displacement x of a particle along the x-axis at time t is given by x=a_1/2t+a_2/3t^2 . Find the acceleration of the particle.

The position of a particle along x-axis at time t is given by x=1 + t-t^2 . The distance travelled by the particle in first 2 seconds is

The displacement of a particle along the x-axis is given by x=3+8t+7t^2 . Obtain its velocity and acceleration at t=2s .

A particle is moving along x-axis. The position of the particle at any instant is given by x= a+bt^(2) where ,a= 6 m and b= 3.5 ms^(-2) 't' is measured in second .Find (i) the velocity of the particle at 1s and (ii) the average velocity between 3s and 6s

The position x of a particle varies with time t as x=at^(2)-bt^(3) . The acceleration at time t of the particle will be equal to zero, where (t) is equal to .

The position x of a particle varies with time t as x=at^(2)-bt^(3) . The acceleration at time t of the particle will be equal to zero, where (t) is equal to .

The displacement x of a particle moving along x-axis at time t is given by x^2 =2t^2 + 6t . The velocity at any time t is

The distance moved by the particle in time is given by x = t^3-12t^2+6t+8 . At the instant when its acceleration is zero, the velocity is (a) 42 (b) -42 (c) 48 (d) -48

If the velocity of a particle moving along x-axis is given as v=(3t^(2)-2t) and t=0, x=0 then calculate position of the particle at t=2sec.

The position of a particle as a function of time t, is given by x(t)=at+bt^(2)-ct^(3) where a,b and c are constants. When the particle attains zero acceleration, then its velocity will be :

OBJECTIVE RD SHARMA ENGLISH-MEAN VALUE THEOREMS-Exercise
  1. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n...

    Text Solution

    |

  2. If the equation a(n)x^(n)+a(n-1)x^(n-1)+..+a(1)x=0, a(1)!=0, n ge2, ha...

    Text Solution

    |

  3. The equation x log x = 3-x has, in the interval (1,3) :

    Text Solution

    |

  4. If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(...

    Text Solution

    |

  5. If alpha beta( alpha lt beta) are two distinct roots of the equation. ...

    Text Solution

    |

  6. If (x) is a function given by f(x) = |{:(sinx , sin a, sin b),(cosx,c...

    Text Solution

    |

  7. The value of c in Lagrange's theorem for the functin f(x)=log sin x in...

    Text Solution

    |

  8. n is a positive integer. If the value of c presecribed in Rolle's th...

    Text Solution

    |

  9. The distance travelled by a particle upto tiem x is given by f(x)=x^(...

    Text Solution

    |

  10. The number of real roots of the equation e^(x-1)+x-2=0 is 1 (b) 2 (...

    Text Solution

    |

  11. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

    Text Solution

    |

  12. If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one rea...

    Text Solution

    |

  13. For the function f(x) = x + 1/x, x in [1,3] , the value of c for me...

    Text Solution

    |

  14. If from Largrange's mean value theorem, we have f'(x(1))=(f'(b)-f(a))...

    Text Solution

    |

  15. Rolle's theorem is applicable in case of phi(x) = a^sin x,a>0 in

    Text Solution

    |

  16. The value of c in Rolle's theorem when f(x)=2x^(3)-5x^(2)-4x+3, x in [...

    Text Solution

    |

  17. When the tangent the curve y=x log (x) is parallel to the chord joinin...

    Text Solution

    |

  18. The value of c in Rolle's theorem for the function f (x) =(x(x+1))/e^x...

    Text Solution

    |

  19. The value of c in Lgrange's Mean Value theorem for the function f(x)...

    Text Solution

    |

  20. In Rolle's theorem the value of c for the function f(x)=x^(3)-3x in th...

    Text Solution

    |