Question

1- The acceleration of a particle is defined by the relation a = 6 ft/s 2. Knowing
that s =-32 ft when t = 0 and v= -6 ft/s when t = 2 s, determine the velocity, the
position, and the total distance traveled when t = 5 s.
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Answer 1

Answer:

The initial velocity of the particle is

v' = -6 - 6.2 = -18 ft/s

at t = 5s, the velocity is v = -18 + 6.5 = 12 ft/s

the position is

$x = - 32 - 18 \times 5 + \frac{1}{2} \times 6 \times 5 {}^{2} = - 47 \: ft$

the total distance traveled is

$s = | \frac{12 {}^{2} - 18 {}^{2} }{2 \times 6} | = 15 \: ft$