CLASSICAL MECHANICS & THERMODYNAMICS - Chapter 1, Exercise 2 Solution
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Finding Distance Using the "No Time" SUVAT Equation

PROBLEM
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A ball is thrown straight up with an initial velocity of 20 m/s. It
decelerates under gravity at -10 m/s^2. Using v^2 = u^2 + 2as, find
how far up the ball travels (s) before its velocity reaches 0 m/s.

SOLUTION
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Using the real SUVAT equation:
    v^2 = u^2 + 2as

Substitute the given values:
    v = 0 m/s   (at the highest point, velocity is momentarily zero)
    u = 20 m/s
    a = -10 m/s^2

    0^2 = 20^2 + 2(-10)s
    0 = 400 - 20s
    20s = 400
    s = 400 / 20
    s = 20 m

ANSWER: The ball travels 20 m upward before its velocity reaches zero.

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WHY THIS WORKS AS AN ANSWER

This equation is the one SUVAT equation with no time (t) term at all,
which makes it the right tool whenever a problem gives distance,
velocities, and acceleration but never mentions how long the motion
took - exactly the situation here, since the problem only asks "how
far" the ball rises, not "how long" it takes to get there. The minus
sign on acceleration correctly represents gravity acting opposite to
the ball's upward motion, steadily removing velocity until it reaches
exactly zero at the peak - the defining condition of "the highest
point" in projectile motion.