Question

the acceleration of aparticle is increasin linerly with time as t= bt the particle start from origin with ainitial velocity v the distance travelled by the particle at any instant t

Answer 1

d2s/dt2 =bt

intigrate

V= ds/dt = bt2/2 +c

at t=0 V=U

so U =0 +c

ds/dt = bt2/2 +U

furthet intigrate

s= b/6 t3 +Ut +d

at t=0 s=0

so d=0

S =b/6 t3 +Ut

Answer 2

S=bvt+1/2ab^2t^2 from formula s=ut+1/2at^2 where u=v from question