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A body moving with initial velocity u accelerates until it attains velocity v within time t. The distance covered is given by which expression?

Physics

ScanSolve AI Answer

Answer

6.0 ms−1\text{6.0 ms}^{-1}

Step-by-step solution

4 steps
  1. Identify the given values.

    The body starts from rest, so the initial velocity is u=0 ms−1u = 0 \text{ ms}^{-1}.
    The acceleration is a=2 ms−2a = 2 \text{ ms}^{-2}.
    The distance travelled is s=9 ms = 9 \text{ m}.
    We need to find the final velocity vv.

  2. Choose the appropriate kinematic equation.

    The kinematic equation that relates initial velocity (uu), final velocity (vv), acceleration (aa), and displacement (ss) is:

    v2=u2+2asv^2 = u^2 + 2as
  3. Substitute the given values into the equation.

    v2=(0 ms−1)2+2(2 ms−2)(9 m)v^2 = (0 \text{ ms}^{-1})^2 + 2(2 \text{ ms}^{-2})(9 \text{ m}) v2=0+36 m2s−2v^2 = 0 + 36 \text{ m}^2\text{s}^{-2} v2=36 m2s−2v^2 = 36 \text{ m}^2\text{s}^{-2}
  4. Solve for vv.

    v=36 m2s−2v = \sqrt{36 \text{ m}^2\text{s}^{-2}} v=6 ms−1v = 6 \text{ ms}^{-1}

    The magnitude of its velocity after travelling 9 m9 \text{ m} is 6.0 ms−1\boxed{\text{6.0 ms}^{-1}}.

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