A lift is going up. The total mass of the lift and the passengers is `2000kg`. The variation of speed of the lift is as shown in the diagram

(a) What will be the tension in the rope pulling the lift at time equal to (i) `1s` (ii) `6s` (iii) `12s`? (b) What will be the average velocity and average acceleration during motion?

Explanation

(a) At `t=0` to `r=4s`
Acceleration`=` slope of `v-t` graph`=(8)/(4)=2m//s^(2)`
At `t=4` to `t=10s`
Acceleration `=0`
At `t=10` to `t=14s`
Acceleration `(8)/(4)=-2m//s^(2)`
For the lift

`T=2000g=2000a`
`T=2000(g+a)`
(i) At `t=1s, a=2m//s^(2)`
`T=2000(g+a)=2000(10+2)=24000N`
(ii) At `t=6s.a=0`
`T=2000(10+0)=2000N`
(iii) At `t=12s,a=-2m//s^(2)`
`T=2000(10-2)=16000N`
(b) At `t=0` to `r=14s`, Displacement`=`area of `v-t` graph
`(1)/(2)(6+14)xx8=80m`
Average velocity `=(80)/(14)=(40)/(7)m//s`
At `t=0` to `t=14s`, Change in velocity`=0`
Average acceleration`=0`