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NEET2015PhysicsMotion in One DimensionActual

The position vector of a particle R → as a function of time is given by: R → = 4 sin ⁡ 2 π t i ^ + 4 c o s ⁡ ( 2 π t ) j ^ Where R is in meters, t is in seconds and i ^ and j ^ denote unit vectors along x- and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

Options

  1. AMagnitude of acceleration vector is v 2 R , where v is the velocity of particle
  2. BMagnitude of the velocity of particle is 8 meter/second
  3. CPatch of the particle is a circle of radius 4 meter
  4. DAcceleration vector is along - R →

Correct answer

B. Magnitude of the velocity of particle is 8 meter/second

Step-by-step solution

x = 4   sin 2 πt y = 4 cos ⁡ ( 2 π t )   Squaring and adding x 2 + y 2 = 4 sin 2 π t 2 + 4 cos 2 π t 2 x 2 + y 2 = 16 This means the particle is moving in a circle V = r w = 2 π 4 = 8 π

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