Question

a particle is initially at rest and move along x-axis is acceleration is there is with time is equal to a=4t if it starts from origin the distance covered by the particle in 3 second is

Answer 1

a=4t
s=ut+0.5*a*t^2
s=0.5*a*t^2            [u=0, Initially particle was at rest]
s=0.5*4t*t^2
s=2t^3
s=2*(3)^3
s=2*27=54m

Answer 2

a = 4t
dv = adt
v = 4t^2 / 2 = 2t^2

v = dx/dt
dx = vdt
x = 2t^3 / 3
At t = 3s
x = 2 × 3^2 / 2
x = 18 m

Distance covered by particle in 3s is 18 m