Reading Fig. 7.39, total energy is 30 J. At P, potential energy is 20 J giving velocity 6.32 m s-1. At Q, potential energy is 30 J giving velocity 0 m s-1. Point R cannot be reached since it requires ...
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From Fig. 7.37, initial speed is 6 m s-1. The trapezoid area gives work done as 150 J, raising kinetic energy to 330 J and final speed to 8.12 m s-1. Acceleration is never negative since force stays positive.
The gain in potential energy is 36250 joules in both cases, calculated by multiplying mass, gravity and height. Gravitational potential energy depends only on vertical height and is completely independent of the path taken.