Question

The acceleration of a particle is increasing linearly with time t as bt. the particle start from origin with an initial velocity v0 the distance travelled by the particle in time t will be

Answer 1

v = u + at

v = at [ u = 0 ]

at = bt

a = b

s = ut + 1/2at²

s = 1/2bt² [ u = 0 ]

Answer 2

Answer:

dvdt=bt⇒dv=bt dt⇒v=bt22+K1 At t=0, v=v0⇒K1=v0 We get v=12bt2+v0

t=0, x=0⇒K2=0 ∴x=16bt3+v0t