Please explain in detail tomake it clear, show all steps so I can understand how

Question

Please explain in detail tomake it clear, show all steps so I can understand how to solve,thanks!
A particle of mass6.3 g, andcharge 20.1 mCmoves in a region of space where the electric field is uniform andis given by Ex = 6.8N/C,Ey = 0, andEz = 0. If thevelocity of the particle at t= 0 is given by vx0 = 178m/s,vy0 = 0, and vz0= 0, what is the speed |v| of the particle at2.46 s?Answer in units of m/s. Please explain in detail tomake it clear, show all steps so I can understand how to solve,thanks!
A particle of mass6.3 g, andcharge 20.1 mCmoves in a region of space where the electric field is uniform andis given by Ex = 6.8N/C,Ey = 0, andEz = 0. If thevelocity of the particle at t= 0 is given by vx0 = 178m/s,vy0 = 0, and vz0= 0, what is the speed |v| of the particle at2.46 s?Answer in units of m/s.

Explanation / Answer

       Given that the mass ofparticle is m = 6.3g = 6.3*10-3 kg        Charge is q = 20.1mC =20.1 *10-3 C        The electric field is E =( -6.8 N/C)i + 0 j+ 0 k          The initial velocityof particle is Vi = (178 m/s )i + 0 j + 0 k        Time taken is t = 2.46s      --------------------------------------------------------------------------          Theaccelaration of the particle is a = F /m                                                                =E*q / m                                                                =  ( -6.8N/C)*(20.1 *10-3 C) i / (6.3*10-3kg) + 0 j+ 0 k                                                                     =( -21.7 m/s2) i + 0 j+ 0 k                      Fromthe equation of motion the final velocity is                           Vf = Vi +a*t                                                =(178 m/s )i + 0 j + 0 k + [( -21.7 m/s2)i + 0 j + 0 k]*2.46s                                 =   (178m/s )i + 0 j + 0 k + ( -53.37 m/s) i +0 j + 0 k                                = (124.63 m/s) i + 0 j + 0 k

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