A vehicle starting from rest and moving under uniform...

A vehicle starting from rest and moving under uniform acceleration along a straight line covers the distance between two points separated by $126 \mathrm{~m}$ in $6 \mathrm{~s}$ and the velocity at the 2 nd point is $30 \mathrm{~m} \mathrm{~s}^{-1}$. Then (a) its velocity at first point is $12 \mathrm{~m} \mathrm{~s}^{-1}$ (b) its acceleration is $2 \mathrm{~m} \mathrm{~s}^{-2}$ (c) the first point is $22 \mathrm{~m}$ from the starting point. (d) it reaches the first point in $4 \mathrm{~s}$ after start.

A vehicle starting from rest and moving under uniform acceleration along a straight line covers the distance between two points separated by $126 \mathrm{~m}$ in $6 \mathrm{~s}$ and the velocity at the 2 nd point is $30 \mathrm{~m} \mathrm{~s}^{-1}$. Then
(a) its velocity at first point is $12 \mathrm{~m} \mathrm{~s}^{-1}$
(b) its acceleration is $2 \mathrm{~m} \mathrm{~s}^{-2}$
(c) the first point is $22 \mathrm{~m}$ from the starting point.
(d) it reaches the first point in $4 \mathrm{~s}$ after start.

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Key Concepts

Uniform Acceleration

Uniform acceleration refers to a constant rate of change of velocity over time. This concept is essential in kinematics because it means that the acceleration does not vary, allowing predictable relationships between displacement, velocity, and time using standard equations of motion.

Kinematic Equations

Kinematic equations provide the mathematical relationships between displacement, initial velocity, final velocity, acceleration, and time in scenarios of uniform acceleration. These equations, such as s = ut + (1/2)at², v = u + at, and v² = u² + 2as, are fundamental tools for solving problems in classical mechanics.

Relationship Between Displacement, Velocity, and Time

This concept involves understanding how the position (displacement) of an object changes as a function of its velocity and the time elapsed, especially under uniform acceleration. It is crucial for analyzing motion and determining unknown variables when some parameters are provided.

Using Given Conditions to Determine Unknown Parameters

In kinematics problems, known conditions like time, displacement, and a specific velocity at a point are used to calculate unknown parameters such as initial velocity and acceleration. This involves setting up and solving equations derived from the kinematic formulas.

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