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The position vector of a particle moving in a plane is given by r = 10*i + (20 - 5t)*j metres, where t is time in seconds. Which of the following statements are correct?

1. (A) The speed of the particle is 10 m/s.
2. (B) The speed of the particle is 5 m/s.
3. (C) The direction of motion of the particle is parallel to the x-axis.
4. (D) The direction of motion of the particle is perpendicular to the x-axis.

Correct answer: (B) The speed of the particle is 5 m/s.

Solution

Velocity v = dr/dt = d(10*i)/dt + d((20-5t)*j)/dt = 0*i + (-5)*j = -5j m/s. Speed = |v| = 5 m/s. Since the velocity is directed along -j (the negative y-direction), it is perpendicular to the x-axis. Statements B and D are correct.

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