Home
Class 12
PHYSICS
The motion of a particle is defined by t...

The motion of a particle is defined by the position vector
`vec(r)=(cost)hat(i)+(sin t)hat(j)` Where `t` is expressed in seconds. Determine the value of `t` for which positions vectors and velocity vector are perpendicular.

A

`1` sec

B

`2` sec

C

for all value of `t`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(v)=(dvecr)/(dt)=-sinthat(i)+costhat(j)`
Here `vec(r).vec(v)=0` so `vec(r)botvec(v)` for all `t`.
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Position vector of a particle is expressed as function of time by equation vec(r)=2t^(2)+(3t-1) hat(j) +5hat(k) . Where r is in meters and t is in seconds. Find the velocity vector

The position vector of a particle is determined by the expression vec r = 3t^2 hat i+ 4t^2 hat j + 7 hat k . The displacement traversed in first 10 seconds is :

A particle is moving with a position vector, vec(r)=[a_(0) sin (2pi t) hat(i)+a_(0) cos (2pi t) hat(j)] . find Distance travelled by the particle in 1 sec is

The projection of a vector vec(r )=3hat(i)+hat(j)+2hat(k) on the x-y plane has magnitude

The position vector of a particle is given by vec(r)=1.2 t hat(i)+0.9 t^(2) hat(j)-0.6(t^(3)-1)hat(k) where t is the time in seconds from the start of motion and where vec(r) is expressed in meters. For the condition when t=4 second, determine the power (P=vec(F).vec(v)) in watts produced by the force vec(F)=(60hat(i)-25hat(j)-40hat(k)) N which is acting on the particle.

Position vector vec(r) of a particle varies with time t accordin to the law vec(r)=(1/2 t^(2))hat(i)-(4/3t^(1.5))hat(j)+(2t)hat(k) , where r is in meters and t is in seconds. Find suitable expression for its velocity and acceleration as function of time.

Position vector vec(r) of a particle varies with time t accordin to the law vec(r)=(1/2 t^(2))hat(i)-(4/3t^(3))hat(j)+(2t)hat(k) , where r is in meters and t is in seconds. Find suitable expression for its velocity and acceleration as function of time

Find the vector equation of a sphere with centre having the position vector hat(i)+hat(j)+hat(k) and sqrt(3) as radius

The position vector of a aprticle is given as vecr=(t^2-t+2)hati+(3t)hatj . The time after which the velocity vector and acceleration vector becomes perpendicular to each other is equal to

The projection of vector, vec(r)=3hat(i)+hat(j)+2hat(k) , on the x-y plane has magnitude-

ALLEN -TEST PAPER-Exercise (Physics)
  1. A stone is thrown at an angle theta to the horizontal reaches a maximu...

    Text Solution

    |

  2. A particle travels with speed 100m//s from the print (10, 20) in a dir...

    Text Solution

    |

  3. The motion of a particle is defined by the position vector vec(r)=(c...

    Text Solution

    |

  4. A car goes A to B along the path with constant accelertion "a" as show...

    Text Solution

    |

  5. A ball is thrown vertically upwards with a velocity v and an initial k...

    Text Solution

    |

  6. In a second ODI match between England and India Bhuwnesh kumar bowled ...

    Text Solution

    |

  7. In a second ODI match between England and India Bhuwnesh kumar bowled ...

    Text Solution

    |

  8. In a second ODI match between England and India Bhuwnesh kumar bowled ...

    Text Solution

    |

  9. A particle is projected vertically upwards with a speed of 16ms^-1. Af...

    Text Solution

    |

  10. The potential energy between two atoms in a molecule is given by U=a...

    Text Solution

    |

  11. An elevator with passengers has a total mass of 800 kg and moves slowl...

    Text Solution

    |

  12. A uniform chain of mass M and length L is lying on a frictionless tabl...

    Text Solution

    |

  13. A body of mass 2 kg is kept on a rough horizontal surface as shown in ...

    Text Solution

    |

  14. A body displaced from (1,1) to (2,2) along the line y=x under the forc...

    Text Solution

    |

  15. A point mass of 0.5 kg is moving along x- axis as x=t^(2)+2t , where, ...

    Text Solution

    |

  16. A mass m is attached to a spring. The spring is stretched to x by a fo...

    Text Solution

    |

  17. A block of mass m is pushed up against a spring, compressing it to a d...

    Text Solution

    |

  18. A body of mass 0.5 kg travels in a straight line with velocity v = ax^...

    Text Solution

    |

  19. One end of a light spring of spring constant k is fixed to a wall and ...

    Text Solution

    |

  20. Select the correct alternative.

    Text Solution

    |