A body covers 30m & 40m during 10th & 15 th second respectively the acceleration and initial body are respectively

Answer 1

the average speed from t = 9 to t = 10 is 30 m/s call it Va
the average speed from t = 14 to t = 15 is 40 m/s Call it Vb
so
x....... v....... t
Xi .....Vi ... ..0
Xa ....30.... 9.5
Xb ....40 ....14.5

If a is constant
v = Vi + at
x = Xi + Vi t + (1/2) a t^2
Xb = Xi + Vi (14.5) + (1/2) a (14.5)^2
Xa = Xi + Vi(9.5) + (1/2) a (9.5)^2
Vb = Vi + a(14.5)
Va = Vi + a(9.5)
---------------------------subtract,
Vb - Va = 40-30 = 10 = a (14.5-9.5) = a (5)
so
a = 2 m/s^2

now work on Vi
Xb - Xa = average speed from t = 9.5 to 14.5 times 5 seconds
= 35 * 5 = 175 m
so
175 = 5 Vi + (1/2)2(14.5^2-9.5^2)
175 = 5 Vi + (210-90)
175 = 5 Vi + 120
Vi = 11 m/s