Physics

Physics

Problem

A car accelerates uniformly from rest at 2.0 m/s22.0\,\text{m/s}^2. How far has the car traveled by the time its speed reaches 24 m/s24\,\text{m/s}? Give your answer in metres.
Intuitive explanation

The key is recognizing that you have constant acceleration, initial velocity, and final velocity—but you don't need time. Use the kinematic equation that links these three quantities directly: v2=v02+2aΔxv^2 = v_0^2 + 2a\Delta x. This avoids the extra step of finding time first and lets you solve for distance in one clean move.

Intuitive explanation

The key is recognizing that you have constant acceleration, initial velocity, and final velocity—but you don't need time. Use the kinematic equation that links these three quantities directly: v2=v02+2aΔxv^2 = v_0^2 + 2a\Delta x. This avoids the extra step of finding time first and lets you solve for distance in one clean move.

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