Cars A, B, and C start from rest at the same location and accelerate for as described…

MATHEMATICS · Subjective · A Level · Mathematics · Kinematics · Kinematics

Problem

Cars A, B, and C start from rest at the same location and accelerate for

6\,\text{s}

as described below, after which they coast at constant speed. • Car A: acceleration is

+2\,\text{m/s}^2

for the entire

6\,\text{s}

. • Car B: acceleration increases linearly from

0\,\text{m/s}^2

t=0

+4\,\text{m/s}^2

t=6\,\text{s}

. • Car C: acceleration is

+3\,\text{m/s}^2

for the first

3\,\text{s}

and

0\,\text{m/s}^2

for the next

3\,\text{s}

. (i) Rank the cars by speed at

t = 6\,\text{s}

, from greatest to least. (ii) Rank the cars by displacement at

t = 6\,\text{s}

, from greatest to least. Provide a brief justification for each ranking.