Question

A lift starts from rest. Its acceleration is plotted against time. When it comes to rest the total distance travelled is

• A. $20\text{m}$
• B. $64\text{m}$
• C. $32\text{m}$
• D. $36\text{m}$

Answer 1

The correct option is B $64\text{m}$

From $0-4\text{s}$ the motion is with constant acceleration, the distance can be calculated from kinematics equation
$S_{0-4}=0+\frac{1}{2}2\times 4^2=16\text{m}$
From $4-8\text{s}$ the motion is with constant velocity,
$v=u+at=0+2\times 4=8\text{m/s}$
$S_{4-8}=v\times t=8\times 4=32\text{m}$
From $8-12\text{s}$ the motion is with constant acceleration, the distance can be calculated from kinematics equation
$S_{8-12}=8\times 4-\frac{1}{2}2\times 4^2=16\text{m}$
Total distance covered $=16+32+16\text{m}=64\text{m}$