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The x and y coordinates of the particle at any time are x = 5t − 2t² and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is

1. 5 m/s²
2. -4 m/s²
3. -8 m/s²
4. 0

Correct answer: -8 m/s²

Solution

The x-coordinate is given as x = 5t − 2t². Differentiating twice with respect to time gives acceleration in the x-direction as aₓ = -4 m/s². The y-coordinate is linear (y = 10t), so its acceleration is zero. The net acceleration is thus -4 m/s².

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