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The coordinates of a particle moving in a plane are given by x(t) = a cos p(t) & y(t) = b sin(pt) where a,b (<a) and ‘p’ are positive constants of appropriate dimensions. Then:-
  • a)
    The path of the particle is an ellipse
  • b)
    The velocity & acceleration of the particles are normal to each other at 
  • c)
    The acceleration of the particle is always directed towards a focus.
  • d)
    The distance travelled by the particle in time interval t = 0 to t =  is ‘a
Correct answer is option 'A,B,C'. Can you explain this answer?
Verified Answer
The coordinates of a particle moving in a plane are given by x(t) = a ...
x = a cos (pt) & y = b sin (pt)

squaring & adding eqn (1) & (2) we get:
  — [.-.path of the particle is an ellipse]
from the given eqn we can find.



⇒ a1 & V1 becomes zero (because cos π/y
0)
Only Vx & ay are left
or we can say that velocity is along negative x-axis and acceleration along y - axis.
Hence at t =  velocity & accleration of the particle are normal to each other. 
So option B is correct
At t = t1 position of the particle 


& acceleration of the particle is 

∴   acceleration of the particle is always directed towards the origin. Hence option C is correct
At t = 0, particle is at (a,0) & at t =  particle is at (0,b)
distance covered in  th of the elliptical path not ‘a’.
Hence Option A, B,C, are correct
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The coordinates of a particle moving in a plane are given by x(t) = a cos p(t) & y(t) = b sin(pt) where a,b (<a) and ‘p’ are positive constants of appropriate dimensions. Then:-a)The path of the particle is an ellipseb)The velocity & acceleration of the particles are normal to each other atc)The acceleration of the particle is always directed towards a focus.d)The distance travelled by the particle in time interval t = 0 to t = is ‘aCorrect answer is option 'A,B,C'. Can you explain this answer?
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The coordinates of a particle moving in a plane are given by x(t) = a cos p(t) & y(t) = b sin(pt) where a,b (<a) and ‘p’ are positive constants of appropriate dimensions. Then:-a)The path of the particle is an ellipseb)The velocity & acceleration of the particles are normal to each other atc)The acceleration of the particle is always directed towards a focus.d)The distance travelled by the particle in time interval t = 0 to t = is ‘aCorrect answer is option 'A,B,C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The coordinates of a particle moving in a plane are given by x(t) = a cos p(t) & y(t) = b sin(pt) where a,b (<a) and ‘p’ are positive constants of appropriate dimensions. Then:-a)The path of the particle is an ellipseb)The velocity & acceleration of the particles are normal to each other atc)The acceleration of the particle is always directed towards a focus.d)The distance travelled by the particle in time interval t = 0 to t = is ‘aCorrect answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The coordinates of a particle moving in a plane are given by x(t) = a cos p(t) & y(t) = b sin(pt) where a,b (<a) and ‘p’ are positive constants of appropriate dimensions. Then:-a)The path of the particle is an ellipseb)The velocity & acceleration of the particles are normal to each other atc)The acceleration of the particle is always directed towards a focus.d)The distance travelled by the particle in time interval t = 0 to t = is ‘aCorrect answer is option 'A,B,C'. Can you explain this answer?.
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