Quick questions on Kinematics: equations of motion, motion under gravity and motion graphs - CCEA A-Level Mathematics

To choose an equation, list the quantities you know and want, then pick the one missing the variable you neither know nor need.

A body moving freely under gravity has constant acceleration $g \approx 9.8\,\text{m s}^{-2}$ downwards (air resistance ignored). Choose a positive direction and keep signs consistent: if up is positive, then $a = -g$. At the highest point of a vertical throw the velocity is momentarily zero, which is the key fact for finding the maximum height.

Decide a positive direction once and stick to it; with up positive, the acceleration is $-9.8\,\text{m s}^{-2}$ and a downward final velocity is negative.

A car travels at constant $15\,\text{m s}^{-1}$ for $12\,\text{s}$. Find the distance. [1 mark]

A ball is dropped from rest. Find its speed after $2\,\text{s}$, taking $g = 9.8\,\text{m s}^{-2}$. [2 marks]

On a velocity-time graph, what does the area under the line represent? [1 mark]