Kinematic Equations — Revision Notes

⚡ 30-Second Revision

Variables — $u$ (initial velocity), $v$ (final velocity), $a$ (constant acceleration), $t$ (time), $s$ (displacement).
Condition — Applicable ONLY for constant acceleration.
Equations

* $v = u + at$ * $s = ut + \frac{1}{2}at^2$ * $v^2 = u^2 + 2as$ * $s_{n^{th}} = u + \frac{a}{2}(2n - 1)$ (Displacement in $n^{th}$ second)

Key Points — Consistent sign conventions, $u=0$ for 'starts from rest', $v=0$ for 'comes to rest', $a=pm g$ for free fall.

2-Minute Revision

Kinematic equations are your go-to tools for analyzing motion when acceleration is constant. Remember the five key variables: $u$ (initial velocity), $v$ (final velocity), $a$ (constant acceleration), $t$ (time), and $s$ (displacement).

The three main equations are $v = u + at$, $s = ut + \frac{1}{2}at^2$, and $v^2 = u^2 + 2as$. A fourth useful equation is $s_{n^{th}} = u + \frac{a}{2}(2n - 1)$ for displacement in a specific second. Always define a positive direction and apply consistent sign conventions for vector quantities ($u, v, a, s$).

For free fall, $a$ becomes $pm g$. When solving problems, identify the three knowns and the one unknown to pick the most efficient equation. Pay attention to keywords like 'starts from rest' ($u=0$) or 'comes to a stop' ($v=0$).

Practice with free fall and multi-stage problems to solidify your understanding.

5-Minute Revision

Kinematic equations are indispensable for NEET physics, specifically for situations where an object moves with constant acceleration. The core idea is to relate the five kinematic variables: initial velocity ($u$), final velocity ($v$), constant acceleration ($a$), time ($t$), and displacement ($s$).

The Four Essential Equations:

1
$v = u + at$ — This equation directly links velocities, acceleration, and time. Use it when displacement is not involved or not required.
2
$s = ut + \frac{1}{2}at^2$ — This is for finding displacement when you know initial velocity, acceleration, and time. It's crucial for problems like calculating the distance covered by an accelerating car.
3
$v^2 = u^2 + 2as$ — This equation is powerful when time is unknown or not needed. It connects velocities, acceleration, and displacement, often used in braking problems or finding maximum height in free fall.
4
$s_{n^{th}} = u + \frac{a}{2}(2n - 1)$ — This specialized equation calculates the displacement covered *only* during the $n^{th}$ second (e.g., the 5th second). Don't confuse it with total displacement after $n$ seconds.

Critical Problem-Solving Steps:

Identify Knowns and Unknowns — List $u, v, a, t, s$ and mark what's given and what needs to be found. Look for implicit information: 'starts from rest' means $u=0$; 'comes to a stop' means $v=0$; 'dropped' means $u=0$ and $a=g$.
Sign Conventions — This is where most errors occur. Choose a positive direction (e.g., upwards or the initial direction of motion). Then, assign positive or negative signs to $u, v, a, s$ based on their direction relative to your chosen positive direction. For free fall, if 'up' is positive, $a=-g$. If 'down' is positive, $a=+g$.
Unit Consistency — Always use SI units (meters, seconds, m/s, m/s$^2$). Convert if necessary.
Equation Selection — Pick the equation that contains your three known variables and the one unknown you want to find. This streamlines the solution process.

Common Applications & Traps:

Free Fall — Frequent questions involve objects falling or thrown vertically. Remember $a=pm g$.
Multi-stage Motion — Break down problems into segments. The final velocity of one segment becomes the initial velocity for the next.
Graphs — Understand that the slope of a $v-t$ graph is acceleration, and the area under a $v-t$ graph is displacement. A straight line on a $v-t$ graph means constant acceleration.
Distance vs. Displacement — Kinematic equations yield displacement ($s$). If an object changes direction, total distance will be different from $|s|$.

Prelims Revision Notes

Kinematic equations are essential for NEET, describing motion under constant acceleration.

Key Variables:

$u$: Initial velocity (m/s)
$v$: Final velocity (m/s)
$a$: Constant acceleration (m/s$^2$)
$t$: Time (s)
$s$: Displacement (m)

Fundamental Equations (for constant $a$):

1
$v = u + at$ — Relates final velocity, initial velocity, acceleration, and time.
2
$s = ut + \frac{1}{2}at^2$ — Relates displacement, initial velocity, acceleration, and time.
3
$v^2 = u^2 + 2as$ — Relates final velocity, initial velocity, acceleration, and displacement (time-independent).
4
$s_{n^{th}} = u + \frac{a}{2}(2n - 1)$ — Displacement covered *only* in the $n^{th}$ second.

Crucial Points for NEET:

Constant Acceleration — These equations are strictly valid only when acceleration is constant. If acceleration varies, calculus is required.
Sign Conventions — Define a positive direction (e.g., upward, rightward). Assign signs to $u, v, a, s$ consistently. If velocity is positive and acceleration is negative, the object is slowing down (decelerating).
Free Fall — For objects under gravity, $a = g$ (if downward is positive) or $a = -g$ (if upward is positive). Use $g approx 9.8,\text{m/s}^2$ or $10,\text{m/s}^2$ as specified.
Keywords

* 'Starts from rest': $u=0$. * 'Comes to rest/stop': $v=0$. * 'Dropped': $u=0$. * 'Maximum height': $v=0$ at the peak.

Graphical Interpretation

* $v-t$ graph: Slope = acceleration, Area = displacement. * $x-t$ graph: Slope = velocity. * A straight line on a $v-t$ graph indicates constant acceleration.

Problem-Solving Strategy

1. List knowns and unknowns. 2. Choose a consistent sign convention. 3. Select the equation that contains the three knowns and the one unknown. 4. Solve algebraically, then substitute values. 5. Check units and the reasonableness of the answer.

Common Traps — Incorrect sign usage, confusing distance with displacement, arithmetic errors, misapplying equations when acceleration is not constant.

Vyyuha Quick Recall

SUVAT is a classic mnemonic for the variables: S (displacement), U (initial velocity), V (final velocity), A (acceleration), T (time). Just remember to pick the equation that leaves out the variable you don't know and don't need!