Question

Give the equations of motion of a particle undergoing retardation along a straight line.

Answer 1

Retardation:

During retardation, the velocity of the particle decreases with time due to which the acceleration becomes negative.

Three equations of motion when the particle is accelerating:

1. The first equation of motion for a particle traveling in a straight line with a constant acceleration is $v=u+at$.
2. The second equation of motion for a particle traveling in a straight line with a constant acceleration is $s=ut+\frac{1}{2}a{t}^2$.
3. The third equation of motion for a particle traveling in a straight line with a constant acceleration is $v^2=u^2+2as$.
4. In these equations, $u$is the initial velocity, $v$ is the final velocity, $a$ is the constant acceleration, $s$ is the displacement and $t$ is the time taken by the particle.

Three equations of motion when the particle is retarding:

1. During retardation, the three equations of motions are only valid if the particle is retarding with a constant acceleration applied in a direction opposite to the direction of motion of the particle. Therefore, the retardation $=-a$.
2. Thus, the first equation of motion becomes $v=u-at$.
3. Thus, the second equation of motion becomes $s=ut-\frac{1}{2}a{t}^2$.
4. Thus, the third equation of motion becomes $v^2=u^2-2as$.

Hence, the equations of motion of a particle undergoing retardation along a straight line are $\mathit{v}\mathbf{=}\mathit{u}\mathbf{-}\mathit{a}\mathit{t}$, $\mathit{s}\mathbf{=}\mathit{u}\mathit{t}\mathbf{-}\frac{\mathbf{1}}{\mathbf{2}}\mathit{a}{\mathit{t}}^{\mathbf{2}}$ and ${\mathit{v}}^{\mathbf{2}}\mathbf{=}{\mathit{u}}^{\mathbf{2}}\mathbf{-}\mathbf{2}\mathit{a}\mathit{s}$.