A 4 kg mass moves under the influence of a force F 4t 3i 3tj

Question

A 4 kg mass moves under the influence of a force vec F = (4t^3hat i - 3that j) N where t is the time in second. If mass starts from origin at t = 0, the velocity and position after t = 2s will be :

DivineJEE · Accepted Answer

vec F = 4t^3hat i - 3that j vec a = fracvec Fm = t^3hat i - (3 / 4)that j x-componenty-componenta_x = t^3a_y = -(3 / 4)t(dv_x / dt) = t^3(dv_y / dt) = -(3 / 4)tintegral _v_x=0^v_x_2 dv_x = integral _t=0^t=2 t^3 dtintegral _0^v_y_2 dv_y = integral _0^2 -(3 / 4)t dtv_x_2 - 0 = [ (t^4 / 4) ]_0^2v_y_2 = -(3 / 4) [ (t^2 / 2) ]_0^2v_x_2 = 4v_y_2 = -(3 / 2) vec v_2 = 4hat i - (3 / 2)hat j x-componenty-componentv_x = (t^4 / 4)v_y = -(3 / 8)t^2integral _0^x_2 dx = integral _0^2 (t^4 / 4) dtintegral _0^y_2 dy = integral _0^2 -(3 / 8)t^2 dtx_2 - 0 = [ (t^5 / 20) ]_0^2y_2 - 0 = -(3 / 8) [ (t^3 / 3) ]_0^2x_2 = (8 / 5)y_2 = -1 vec r = (8 / 5)hat i - hat j

Explanation

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