a 125 gram mass starts from rest at the origin (at t = 0) andmoves with a veloci

Question

a 125 gram mass starts from rest at the origin (at t = 0) andmoves with a velocity of v = 2 t i - t3 j (tis in s and v is in m/s). a) what is the magnitude of the velocity at t = 2s ? b) what is the magnitude of the acceleration of the mass at t= 2s? c) what is the position of the mass as a function of time, r (t ) ? d) what is the magnitude of the force on the mass at t2s? please answer all questions. Thanks a 125 gram mass starts from rest at the origin (at t = 0) andmoves with a velocity of v = 2 t i - t3 j (tis in s and v is in m/s). a) what is the magnitude of the velocity at t = 2s ? b) what is the magnitude of the acceleration of the mass at t= 2s? c) what is the position of the mass as a function of time, r (t ) ? d) what is the magnitude of the force on the mass at t2s? please answer all questions. Thanks

Explanation / Answer

mass m = 125 g = 0.125 kg initial velocity u = 0 velocity v= 2t i -t^3 j (a). velocity at t = 2 s is v = 4 i - 8 j magnitude = [ 4 ^ 2 + -8^2 ] = 8.944 m / s (b). accleration a = dv / dt = 2 i -3t^2 i acleration at t= 2 s is a = 2 i - 12 j magnitude = [2^2 + -12^2 ] = 12.165 m / s ^ 2 (c). position r (t ) = integral v(t) dt                           = 2(t^2 / 2 ) i - ( t^ 4 / 4 ) j+C                           = t^2 i -0.25 t^4 + C at t= 0   r = 0 So, C = 0 therefore position r ( t ) = t ^ 2 i -0.25 t ^ 4 j (d). force at t= 2 is   m * acclerationa t t= 2                              = 0.125 kg * 12.165 m / s ^ 2 = 1.52 N

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