As shown in the figure a particle is released from P. It...

As shown in the figure a particle is released from $P$. It reaches at point $\mathrm{Q}$ at time $\mathrm{t}_{1}$ and reaches at point $\mathrm{R}$ at time $\mathrm{t}_{2}$ so $\left(\mathrm{t}_{1} / \mathrm{t}_{2}\right)=\ldots$ $(\mathrm{A})+(1 / 3)$ (B) $-(5 / 6)$ (C) $(2 / 1)$ (D) $(4 / 1)$

As shown in the figure a particle is released from $P$. It reaches at point $\mathrm{Q}$ at time $\mathrm{t}_{1}$ and reaches at point $\mathrm{R}$ at time
$\mathrm{t}_{2}$ so $\left(\mathrm{t}_{1} / \mathrm{t}_{2}\right)=\ldots$
$(\mathrm{A})+(1 / 3)$
(B) $-(5 / 6)$
(C) $(2 / 1)$
(D) $(4 / 1)$

Key Concepts

Time-Displacement Relationship

In uniformly accelerated motion from rest, the distance travelled is directly linked to the square of the time elapsed. This quadratic relationship means that if you know the time taken for one segment of the motion, you can predict how the displacement scales for different time intervals, which is a critical reasoning tool in many motion problems.

Gravitational Motion

Gravitational motion involves analyzing how objects move under the influence of gravity, which imparts a nearly constant acceleration near the Earth's surface. This concept is widely applied in physics to understand free-fall, projectile motion, and similar phenomena, emphasizing the predictable nature of motion when gravity is the primary force.

Uniform Acceleration

This concept refers to motion where the acceleration remains constant over time. It is fundamental in analyzing scenarios where the only force acting is gravity, such as objects in free fall. The assumption of constant acceleration simplifies the mathematical treatment of a particle's motion, allowing the use of standard kinematic equations.

Kinematic Equations

Kinematic equations are the mathematical tools used to relate displacement, velocity, acceleration, and time in motions with constant acceleration. Equations like s = ut + ½at² and v² = u² + 2as are essential for deriving relationships between time intervals and distances traveled, helping to solve problems in mechanics without needing to reference complex forces.

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