A bus and a car start from rest and run along a straight...

A bus and a car start from rest and run along a straight linc with constant acccleration of $2 \mathrm{~m} / \mathrm{s}^{2}$ and $3 \mathrm{~m} / \mathrm{s}^{2}$ respectively, with the car behind the bus at distance of $100 \mathrm{~m}$. How long will it take beforc both the bus and car travel side by sidc?

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Key Concepts

Uniform Acceleration

This concept involves objects moving with a constant acceleration, which means the rate of change of velocity remains steady over time. It is fundamental in solving issues where velocity and displacement are time-dependent, providing a framework to determine various motion parameters from a known acceleration.

Kinematic Equations

Kinematic equations are a set of formulas that relate displacement, initial velocity, acceleration, and time for objects moving with constant acceleration. They are essential for solving motion problems by allowing calculation of unknown parameters when given sufficient information about other variables.

Relative Motion Analysis

Relative motion analysis involves examining the movement of one object with respect to another, which is particularly useful when two objects start from different positions or have different accelerations. By comparing their distances as functions of time, it helps to determine when the positions of the objects will coincide.

Quadratic Equations in Motion

When solving for the time at which two objects meet in problems involving constant acceleration, the equations used can lead to a quadratic equation in time. Solving these quadratic equations is necessary to determine the correct value of time for the event when the positions of the objects become equal.

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