How to Calculate Speed at Different Points Using Conservation of Energy?

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To calculate the speed of a block at different points using conservation of energy, one must consider both kinetic and potential energy. The initial speed of the block at Point A is 7 m/s, and its mass is 8 kg. The problem requires determining the speed at Points B and C while neglecting friction. The approach involves using gravitational potential energy to assess changes in speed as the block moves. The relevant equations for kinetic and potential energy will guide the calculations.
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INTRODUCTION:
This is a problem from my Introduction to Physical Science class using "Conceptual Physics" 10th Ed.by Paul G. Hewitt

EXACT PROBLEM:
"The block in the figure at the right has a mass of 8kg and an initial speed of 7 m/s at Point A. Neglect frictional forces."

PROBLEMS FACED:
a) What will be its speed when it reaches Point B?
b) What will be its speed when it reaches Point C?

MY THOUGHTS:
Should I be looking for kinetic energy? What am I doing here?
 
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This is the diagram:

physics-1.jpg
 
Kinetic and Potential energy. Looks like an application of work energy/
 
I would think that speed is in this case equal to the initial plus any provided by external forces. In this case, the only other force is gravity. So as you suggest use th potential energy from gravity to add to the initial velocity. Whats that eqn?
 
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