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This paper focuses on acceleration trajectory shaping using model predictive control for autonomous vehicles. The proposed method employs two types of constraints for the shaping: hard constraints, which must be satisfied and soft constraints, which can be relaxed if required. The soft constraints require that the acceleration trajectory be shaped into the desired piece-wise linear function of time, while collision avoidance is guaranteed by utilizing hard constraints. Since we can specify the desired level of acceleration and jerk directly, it becomes straightforward to design and adjust the shape of the trajectory. Further, fast and stable solvers are available, since the optimization problem is formulated in convex quadratic programming. We employ a desired trajectory with constant acceleration (deceleration) as a typical target, and validate the reshaping performance and verify the feasibility of the method through experiments with real vehicles. Two experimental scenarios are considered to ensure the compatibility of trajectory shaping and collision avoidance: sudden braking of a preceding vehicle and cutting-in by a slow-moving vehicle. The experimental results show that the proposed method successfully shaped the trajectory satisfying collision avoidance, while soft constraints for shaping were appropriately relaxed as demanded, which supports the effectiveness of the proposed method.