Figure given here shows the variation of velocity of a particle with time.

Find the following:
(i) Displacement during the time intervals.
(a) 0 to 2 sec., (b) 2 to 4 sec. and (c) 4 to 7 sec
(ii) Accelerations at
(a)t = 1 sec, (b) t = 3 sec. and (c)t = 6 sec.
(iii) Average acceleration
(a) between t = 0 to t = 4 sec.
(b) between t = 0 to t = 7 sec.
(iv) Average velocity during the motion.

Answer

i) a) 8m b) 16m c) 12m
ii) a) `4ma^(-2)` b) 0 c) `-8//3ms^(-2)`
iii) a) `2m//s^(2)` b) 0 iv) `(36)/(7)ms^(-1)`

Explanation

i) displacement = Area enclosed between `v-t` graph and time axis.
ii) Acceleration = slope of `v-t` curve
iii) Average acceleration = `("Total change in velocity")/("Total time")`
(iv) Average velocity = `("Total displacement")/("Total time")`