Assertion (A): An object moving with a velocity of magnitude \(10 \text{ m/s}\) is subjected to a uniform acceleration \(2 \text{ m/s}^2\) at right angle to the initial motion. Its velocity after \(5s\) has a magnitude nearly \(14 \text{ m/s}\).
Reason (R): The equation \(\vec{v} = \vec{u} + \vec{a}t\) can be applied to obtain \(\vec{v}\) if \(\vec{a}\) is constant.
Solution:
Assertion (A): Given \(u = 10 \text{ m/s}\), \(a = 2 \text{ m/s}^2\), \(t = 5 \text{ s}\). Since \(\vec{u}\) and \(\vec{a}\) are perpendicular, the final velocity magnitude is \(|\vec{v}| = \sqrt{u^2 + (at)^2} = \sqrt{10^2 + (2 \times 5)^2} = \sqrt{100+100} = \sqrt{200} \approx 14.14 \text{ m/s}\). So (A) is true.
Reason (R): The equation \(\vec{v} = \vec{u} + \vec{a}t\) is valid when acceleration \(\vec{a}\) is constant. So (R) is true.
(R) correctly explains (A) as the formula is used due to constant acceleration.
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