A certain elevator cab has a total run of 198 m and a maximum speed is 317 m/min, and it accelerates from rest and then back to rest at 1.11 m/s2. (a) How far does the cab move while accelerating to full speed from rest? (b) How long does it take to make the nonstop 198 m run, starting and ending at rest?

Respuesta :

Answer:

Explanation:

Given

Total run=198 m

maximum speed=317 m/min=5.28 m/s

acceleration[tex]=1.11 m/s^2[/tex]

(a)Distance traveled while  accelerating

[tex]v^2-u^2=2as[/tex]

[tex](5.28)^2-0=2\times 1.11\times s[/tex]

s=12.57 m

time taken

v=u+at

[tex]5.28=0+1.11\times t[/tex]

t=4.75 s

(b)Time taken to cover 198 m

if car takes 12.57 m & 4.75 s to reach max speed so it also takes 12.57 m and 4.75 s to stop from max speed

Distance traveled with max speed=198-25.14=172.86 m

time taken[tex]=\frac{172.86}{5.28}=32.73 s[/tex]

total time=4.75+32.73+4.75=42.25 s