zigya tab
The position of a particle is given by,
bold r bold space bold equals bold space 3.0 space straight t space straight i with hat on top space minus space 2.0 space straight t squared space straight j with hat on top space plus space 4.0 space straight k with hat on top space straight m
where t is in seconds and the coefficients have the proper units for r to be in metres.
(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

 


Velocity space vector space is comma space straight v with rightwards harpoon with barb upwards on top space equals space 3.0 space straight i with hat on top space minus space 4.0 space straight j with hat on top space

At space straight t space equals space 2.0 space sec

straight v with rightwards harpoon with barb upwards on top space equals space 3.0 space straight i with hat on top space minus 8.0 space straight j with hat on top space

Magnitude space of space velocity comma space open vertical bar straight v with rightwards harpoon with barb upwards on top close vertical bar space equals space square root of left parenthesis 3 right parenthesis squared plus left parenthesis negative 8 right parenthesis squared end root space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals square root of 73 space equals 8.54 space straight m divided by straight s

Direction comma space straight theta space equals space tan to the power of negative 1 end exponent space open parentheses straight v subscript straight y over straight v subscript straight x close parentheses space
space space space space space space space space space space space space space space space space space space space space space space equals space tan to the power of negative 1 end exponent space open parentheses negative 8 over 3 close parentheses space

space space space space space space space space space space space space space space space space space space space space space space equals negative space space tan to the power of negative 1 end exponent space left parenthesis 2.667 right parenthesis space

space space space space space space space space space space space space space space space space space space space space space equals space minus 69.45 to the power of straight o

Negative space sign space indicates space that space the space direction space of space
velocity space is space below space the space straight x minus axis.
119 Views

Read the statement below carefully and state, with reasons, if it is true or false:

A.

The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector

A. TRUE

Tips: -

The direction of acceleration vector in a uniform circular motion is directed towards the centre of circular path. It is constantly changing with time. The resultant of all these vectors will be zero vector.
117 Views

Advertisement

Read the statement below carefully and state, with reasons, if it is true or false:

A.

The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point


A. TRUE

Tips: -

Because while leaving the circular path, the particle moves tangentially to the circular path.
108 Views

Advertisement
The position of a particle is given by
bold r bold space bold equals bold space 3.0 space straight t space straight i with hat on top space minus space 2.0 space straight t squared space straight j with hat on top space plus space 4.0 space straight k with hat on top space straight m
where t is in seconds and the coefficients have the proper units for r to be in metres.

(a) Find the v and a of the particle? 

straight a right parenthesis thin space
straight v with rightwards harpoon with barb upwards on top left parenthesis straight t right parenthesis space equals space left parenthesis 3.0 space straight i with hat on top space minus space 4.0 straight t space straight j with hat on top right parenthesis

straight a space equals space minus 4.0 space straight j with hat on top space

Position space of space the space particle space is space given space by comma space

bold r bold space bold equals bold space 3.0 space straight t space straight i with hat on top space minus space 2.0 space straight t squared space straight j with hat on top space plus space 4.0 space straight k with hat on top space straight m

Velocity comma space straight v with rightwards harpoon with barb upwards on top equals fraction numerator straight d straight r with rightwards harpoon with barb upwards on top over denominator dt end fraction equals straight d over dt left parenthesis bold space 3.0 space straight t space straight i with hat on top space minus space 2.0 space straight t squared space straight j with hat on top space plus space 4.0 space straight k with hat on top space right parenthesis

therefore space straight v with rightwards harpoon with barb upwards on top space equals space 3.0 space straight i with hat on top minus space 4.0 straight t space space straight j with hat on top

Acceleration space of space the space particle space is space given space by comma

straight a with bar on top space equals space fraction numerator straight d straight v with rightwards harpoon with barb upwards on top over denominator dt end fraction space equals space straight d over dt open parentheses space 3.0 space straight i with hat on top minus space 4.0 straight t space space straight j with hat on top close parentheses space

straight a with bar on top space equals space minus space 4.0 space space straight j with hat on top space
103 Views

Read the statement below carefully and state, with reasons, if it is true or false: 

A.

(a) The net acceleration of a particle in circular motion is always along the radius of
the circle towards the centre


A. FALSE
The net acceleration of a particle is towards the centre only in case of a uniform circular motion. 

Tips: -

The net acceleration of a particle is towards the centre only in case of a uniform circular motion.
113 Views

Advertisement