Home
Class 11
PHYSICS
The position x of a particle varies with...

The position x of a particle varies with time t according to the relation `x=t^3+3t^2+2t`. Find the velocity and acceleration as functions of time.

Text Solution

AI Generated Solution

To solve the problem, we need to find the velocity and acceleration of a particle whose position \( x \) varies with time \( t \) according to the equation: \[ x = t^3 + 3t^2 + 2t \] ### Step 1: Find the Velocity ...
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 2.5|2 Videos

  • ARCHIVES 2 VOLUME 6

    CENGAGE PHYSICS ENGLISH|Exercise Integer|4 Videos

  • CALORIMETRY

    CENGAGE PHYSICS ENGLISH|Exercise Solved Example|13 Videos

Similar Questions

Explore conceptually related problems

The acceleration of a particle varies with time t seconds according to the relation a=6t+6ms^-2 . Find velocity and position as funcitons of time. It is given that the particle starts from origin at t=0 with velocity 2ms^-1 .

The position of a particle varies with time according to the relation x=3t^(2)+5t^(3)+7t , where x is in m and t is in s. Find (i) Displacement during time interval t = 1 s to t = 3 s. (ii) Average velocity during time interval 0 - 5 s. (iii) Instantaneous velocity at t = 0 and t = 5 s. (iv) Average acceleration during time interval 0 - 5 s. (v) Acceleration at t = 0 and t = 5 s.

The acceleration a of a particle starting from rest varies with time according to relation, a=alphat+beta . Find the velocity of the particle at time instant t. Strategy : a=(dv)/(dt)

The acceleration of a'particle starting from rest, varies with time according to the relation a=kt+c . The velocity of the particle after time t will be :

The acceleration of a particle which starts from rest varies with time according to relation a=2t+3. The velocity of the particle at time t would be

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

If the displacement of a particle varies with time as x = 5t^2+ 7t . Then find its velocity.

A particle move a distance x in time t according to equation x = (t + 5)^-1 . The acceleration of particle is alphaortional to.

CENGAGE PHYSICS ENGLISH-BASIC MATHEMATICS-Exercise 2.6
  1. The displacement of a particle is given by y=(6t^2+3t+4)m, where t is ...

    Text Solution

    |

  2. The velocity of a particle is given by v=12+3(t+7t^2). What is the acc...

    Text Solution

    |

  3. A particle starts from origin with uniform acceleration. Its displacem...

    Text Solution

    |

  4. The acceleration of a particle is given by a=t^3-3t^2+5, where a is in...

    Text Solution

    |

  5. A particle starts moving along the x-axis from t=0, its position varyi...

    Text Solution

    |

  6. A particle moves along the x-axis obeying the equation x=t(t-1)(t-2), ...

    Text Solution

    |

  7. The speed of a car increases uniformly from zero to 10ms^-1 in 2s and ...

    Text Solution

    |

  8. A car accelerates from rest with 2ms^-2 for 2s and then decelerates co...

    Text Solution

    |

  9. A stationary particle of mass m=1.5kg is acted upon by a variable forc...

    Text Solution

    |

  10. The displacement of a body at any time t after starting is given by s=...

    Text Solution

    |

  11. A particle moves along a straight line such that its displacement at a...

    Text Solution

    |

  12. The displacement x of a particle moving in one dimension under the act...

    Text Solution

    |

  13. The position x of a particle varies with time t according to the relat...

    Text Solution

    |

  14. The displacement of a particle along the x-axis is given by x=3+8t+7t^...

    Text Solution

    |

  15. The acceleration a in ms^-2 of a particle is given by a=3t^2+2t+2, whe...

    Text Solution

    |

  16. The displacement x of a particle along the x-axis at time t is given b...

    Text Solution

    |

  17. A particle moves along a straight line such that its displacement at a...

    Text Solution

    |

  18. The acceleration of a bus is given by ax(t)=at, where a=1.2ms^-2. If...

    Text Solution

    |

  19. The acceleration of a motorcycle is given by ax(t)=At-Bt^2, where A=1....

    Text Solution

    |

  20. The acceleration of a particle varies with time t seconds according to...

    Text Solution

    |