The displacement x of a particle varies with time as sqrt(x) = 2t + 5. What is the nature of the motion of the particle?

Uniformly accelerated
Uniform motion
Retarded

Correct answer: Uniformly accelerated

Solution

From sqrt(x) = 2t+5: x = (2t+5)² = 4t² + 20t + 25. Velocity v = 8t + 20 (increases with time). Acceleration a = 8 m/s² (constant and positive). This is uniformly accelerated motion.

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