At t=0, a particle start from rest at x=0 y=0 and move in thexy plane with accel

Question

At t=0, a particle start from rest at x=0 y=0 and move in thexy plane with acceleration a=(4.0i +3.0j)m/s^2 . assume t is insecond. Determine the x and y component of the velocity as thefunction of time. Determine the speed and the position of the particleas a function of time. At t=0, a particle start from rest at x=0 y=0 and move in thexy plane with acceleration a=(4.0i +3.0j)m/s^2 . assume t is insecond. Determine the x and y component of the velocity as thefunction of time. Determine the speed and the position of the particleas a function of time.

Explanation / Answer

Acceleration a=(4.0i +3.0j)m/s^2 So, velocity v = integral a   dt                      = 4 t i + 3 t j + C where C = integration constant at time t = 0 , velocity v = 0 m / s substitue this in above we get velocity function v = 4 ti + 3 t i Position function   r = integral v dt                              = 2 t^2   i + ( 3/2 ) t ^ 2 j + C ' using the condition we get C ' = 0 So, r =  2 t^2   i + ( 3/2 ) t ^2 j

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