As per Newton's II law we can say
Force applied is rate of change of momentum
[tex]F = \frac{dP}{dt}[/tex]
here we have
[tex]dP = P_f - P_i[/tex]
[tex]dP = mv_f - mv_i[/tex]
given that
m = 0.25 kg
[tex]v_f = 40 m/s[/tex]
[tex]v_i = 0[/tex]
F = 460 N
now by above equation
[tex]460 = \frac{0.25(40 - 0)}{t}[/tex]
[tex]t = \frac{10}{460} = 0.022 s[/tex]
so it required 0.022 s of contact time
