The speed time graph of a particle moving along a fixed direction is as shown in the figure. Obtain the distance travelled by the particle from,
(a) t = 0 to 10s
(b) t= 2s to 6s
(c) What is the average speed of the particle over the intervals in (a) and (b)?

Explanation

(a) Distance covered
`=(1)/(2)bh =(1)/(2)xx10xx12=60m`
`"displacement"=[(1)/(2)bar(OC)xxbar(AC)]-[1//2 bar(B)C xx bar(A)C]`
= 0
(b) Distance covered from `t=2s " to " t = 6s`
`="Area ACFD "+"Area AENC "v=o+at`
`=(1)/(2)(5-3)(4.8+12)+(1)/(2)(6-5)(12+9.6)" "therefore a=(v)/(t)=(12)/(5)`
`=25.2+10.8" "a=2.4ms^(-1)`
`=36m" "v_(D)=(2.4)(2)=4.8 ms^(-1)`
(c) `"Average speed "=("total distance")/("time taken")=((1)/(2)xx10xx12)/(10)" "v_(B)=12-2.4(1)=9.6 ms^(-1)`
`=6ms^(-1)`