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A particle starts from rest and travels a total distance of 18m along a straight path. The first half of the distance was travelled with a uniform acceleration of $2m{s^{ - 2}}$ and the rest uniform velocity. The average velocity for the whole journey is (in $m{s^{ - 1}}$)
A) 3
B) 4
C) 6
D) 9

Last updated date: 17th Jul 2024
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Hint: When the motion is in uniform acceleration, the velocity is constant and when the motion is in uniform velocity, the displacement is constant and the acceleration is zero. This fact must be applied while solving this problem for calculating the average velocity.

Complete step by step answer:
Consider a particle that starts from rest. The total distance covered by the particle,
$D = 18m$
The first half of the distance is covered in the uniform acceleration of $2m{s^{ - 2}}$. This means that the acceleration of the particle throughout the distance is constant and thus, the velocity of the particle is constant.
The distance covered, $s = \dfrac{{18}}{2} = 9m$
Since, the body starts from the rest, $u = 0$
The final velocity v after covering the half distance, is given by the equation:
$\Rightarrow {v^2} - {u^2} = 2as$
Substituting the values of u, a and s –
$\Rightarrow {v^2} - 0 = 2 \times 2 \times 9$
$ \Rightarrow v = \sqrt {2 \times 2 \times 9} $
$ \Rightarrow v = 2 \times 3 = 6m{s^{ - 1}}$
Thus, the velocity of the particle picked after the half distance is equal to 6m/s. Given that the rest of the journey is covered with a uniform velocity, the velocity will remain the same i.e., 6m/s and it will not vary because during the uniform velocity, the acceleration is equal to zero.
Hence, the average velocity of the particle throughout the journey will be equal to 6m/s since there is no change in the velocity after the half-distance.

Hence, the correct option is Option C.

Note: When a body is in motion with uniform velocity, it implies that there is no external force acting on the body. This is because the force acted on a body is equal to the product of the mass and the acceleration. Thus, the force acted on the body is zero, if the value of acceleration is zero.