Kinematics-5

Let the motion be only along x axis then:

v is proportional to x

=> v = kx (k is constant)

=>dx/dt = kx

=> ∫dx/x = k∫dt

=> ln|x| = kt ....(1)

putting proper limits :

ln|4/2| = 10k

=> k = ln(2)/10 s-1

Substituting (1) from t=0 to t=5s we get

=> ln|x/2| = (ln(2)/10)x5

=> ln|x| - ln(2) = ln(2)/2

=> ln|x| = ln(2)[ 1 + 1/2 ]

=> ln|x| = ln(23/2)

=> x = 23/2 m = 2.82 m [ans]