Do the math. Calculate the motor top speed and acceleration you need to achieve that movement profile. Work out the moment of inertia of the load as seen by the motor, add the moment of inertia of the rotor of a candidate motor, then from the acceleration required you can work out the motor torque needed. If your candidate motor provides enough torque with an adequate safety margin (I suggest at least 2x), then all that is left is to work out what drive voltage you need to achieve the required speed. Apart from this last step, it is all basic Newtonian mechanics.
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