Grade 11 Physics · Displacement
The rectangle and the triangle
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The rectangle and the triangle

The third machine: d=v0t+12at2d = v_0 t + \tfrac{1}{2}at^2 (read aloud: d equals v-nought t, plus one-half a t-squared — and yes, v0v_0 is said “v-nought”), for anything that enters at one speed and accelerates as it goes. The picture explains the half: distance is the area under the speed line. Steady v0v_0 draws a rectangle, area v0tv_0 t. The gained speed draws a triangle on top — and a triangle holds HALF its box, 12at2\tfrac{1}{2}at^2.

Forget the half and every answer lands too far. And run the L3 check before computing: (m/s)s=m\mathrm{(m/s)\,s = m} and (m/s2)s2=m\mathrm{(m/s^2)\,s^2 = m} — both terms cancel to metres, so the rearrangement can face the numbers.