Home
Class 12
PHYSICS
The position of a particle is given by ...

The position of a particle is given by
`r = 3t hati +2t^(2) hatj +8 hatk`
where, t is in seconds and the coefficients have the proper units for r to be in metres.
(i) Find v (t) and a(t) of the particles.
(ii) Find the magnitude and direction of v(t) and a(t) at `t = 1s`.

Text Solution

Verified by Experts

`v(t) (dr)/(dt) =d/t(3.0 hati +2.0t^(2)hatj + 5.0hatk)=3.0hati + 4.0hatj`
`a(t) =(dv)/(dt) =+4.0 hatj, a=4.0 ms^(-2)` along y-direction
(b) At t=1.0 s, `v=3.0hati + 4.0hatj`
It.s magnitude is `v=sqrt(3^(2) + 4^(2)) =5.0 ms^(-1)`
and direction is
`theta = tan^(-1)(v_(y)/v_(x)) = tan^(-1)(4/3) = 53^(@)` with x-axis.
Promotional Banner

Topper's Solved these Questions

  • MOTION IN A PLANE

    AAKASH SERIES|Exercise SHORT ANSWER TYPE QUESTIONS|6 Videos

  • MOTION IN A PLANE

    AAKASH SERIES|Exercise VERY SHORT ANSWER TYPE QUESTIONS|10 Videos

  • MOTION IN A PLANE

    AAKASH SERIES|Exercise EXERCISE-3 (Circular Motion)|7 Videos

  • MOTION IN A STRAIGHT LINE

    AAKASH SERIES|Exercise very Short answer type question|15 Videos

Similar Questions

Explore conceptually related problems

The position of a particle is given by r=3.0thati+2.0t^(2)hatj+5.0 hatk . Where t is in seconds and the coefficients hav the proper units for r to be in matres. (a) find v(t) and a(t) of the particle (b). Find the magnijtude of direction of v(t) or t=1.0 s

Position vector of a particle is given as r = 2t hati +3t^(2) hatj where t is in second and the coefficients have the proper units, for r to be in metres. (i) Find instantaneous velocity v(t) of the particle. (ii) Find magnitude and direction of v(t) at t = 2s

The position of a particle is given by vecr = 3t hati + 2t^(2) hatj + 5hatk , where t is in seconds and the coefficients have the proper units for vecr to be in meters. The direction of velocity of the particle at t = 1 s is

The position of a particle is given by vec r= 3.0 t hat i - 2.0 t^2 hat j + 4.0 hat k m , where (t) in seconds and the coefficients have the proper units for vec r to be in metres. (a) Find the vec v and vec a of the particle ? (b) What is the magnitude and direction of velocity of the particle at t= 2 s ?

The position of of a particle is given by vec r =3.0 t hat I + 2.0 t^(2) hat j+ 5.0 hat k wher (t) in seconds and the coefficients have the proper units . Find the velocity and acceleration of the particle in magnitude and direction at time t=3.0 s

The position of a particle is given by x=2(t-t^(2)) where t is expressed in seconds and x is in metre. The particle

The position of a particle is given by vec r =(8 t hati +3t^(2) hatj +5 hatk) m where t is measured in second and vec r in meter. Calculate, direction of the velocity at t = 1 s

The position of a particle is expressed as vecr = ( 4t^(2) hati + 2thatj) m, where t is time in second. Find the velocity o the particle at t = 3 s

The position of a particle is expressed as vecr = ( 4t^(2)hati + 2thatj) m. where t is time in second. Find the acceleration of the particle.

The position of a particle is given by vec r =(8 t hati +3t^(2) +5 hatk) m where t is measured in second and vec r in meter. Calculate, the magnitude of velocity at t = 5 s,