Home
Class 12
MATHS
A particle moves along a straight line a...

A particle moves along a straight line according to the law `s=t^3-3t^2+5t`. Find its velocity and acceleration at the end of 1 sec.

Text Solution

Verified by Experts

`s=t^3-3t^2+5trArr(ds)/(dt)=3t^2-6t+5rArr(d^2s)/(dt^2)=6t-6` At the end of 1 sec The velocity `=(ds)/(dt)]_(r=1)=2` The acceleration `=(d^2s)/(dt^2)]_(t=1)=0`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    MBD PUBLICATION|Exercise QUESTION BANK|127 Videos
  • TRIGONOMETRIC FUNCTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|267 Videos

Similar Questions

Explore conceptually related problems

A body moving along a straight line has its displacement in m given by s=3+2t+ 4t^2 . Find its velocity after 2s and the acceleration.

A particle moves in x - y plan according to equation x = 4t^2 + 5t + 16 and y = 5t. The acceleration of particle must be

A particle moves in x-y plane according to equations x=4t^2+5t+16 and 6y=5t . What is the acceleration of the particle?

A particle of mass 6 kg moves accordings to the law x=0.2 t^2-0.02 t^3 . Find the work done by the force in first 4 sec.

A particle moves along a straight line such that its displacement at any time t is given by S= (t^3-3t^2+2) m What is the displacement when the acceleration is zero ?

A body moves along a straight line with acceleration 3m/s^2 for 2 seconds and then with acceleration 4 m/s^2 for 3 seconds . What is the average acceleration

The acceleration of a particle starting from rest varies with time according to the relation a=-sw^2 sin wt The displacement of the particle at time 't' will be

A point moves in a straight line so that its displacement x m at time t sec is given by x^2=1+t^2 what is the acceleration in m//sec^2 in time t.

MBD PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. Find the rate of change of the area of circle w.r.t.r when r=8 cm.

    Text Solution

    |

  2. The side of a sqart is increasing at the rate of 0.1 cm//sec and at th...

    Text Solution

    |

  3. A particle moves along a straight line according to the law s=t^3-3t^...

    Text Solution

    |

  4. Show that the function f(x)=1/x is decreasing in (0,oo).

    Text Solution

    |

  5. Find the intervals where the function f(x)=x^3-12x+10 is increasing.

    Text Solution

    |

  6. Find the slope of the normal to the curve y=xe^-x at x=2.

    Text Solution

    |

  7. Find the angle between the tangents to the curve y=x^2-5x+6 at the poi...

    Text Solution

    |

  8. Find the point on the curve y^2 - x^2 + 2x - 1 =0 where the tangent ...

    Text Solution

    |

  9. Find the points on the curve 9y^2=x^2, where normal to the curve makes...

    Text Solution

    |

  10. If y=x^4-12 and if x changes from 2 to 1.99, find the approximate erro...

    Text Solution

    |

  11. Using differential find the value of sqrt(16.2).

    Text Solution

    |

  12. Show that f(x)=x^3-6x^2+24x+4 has neither a maximum nor a minimum valu...

    Text Solution

    |

  13. Find the points where f(x)=8x^2-x^4-4 has local maximum or minimum.

    Text Solution

    |

  14. Find the absolute maximum and absolute minimum value of the function f...

    Text Solution

    |

  15. Find the absolute maximum and absolute minimum value of f(x)=x-x^3 in ...

    Text Solution

    |

  16. Using mean value theorem, prove that sin xltx,in(0.pi//2).

    Text Solution

    |

  17. Write antiderivative of tan^2x

    Text Solution

    |

  18. Write the vale of intxa^(x^(2+1))dx

    Text Solution

    |

  19. Write the vale of intsqrt(1-cos2x)dx

    Text Solution

    |

  20. If f'(x)= e^x+1/(1+x^2),what is f(x) ?

    Text Solution

    |