Question

The acceleration of a particle is increasing linearly with time t as bt. The particle starts from origin with an initial velocity u. The distance travelled by the particle in time t will be?

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