Respuesta :
Answer:
velocity after 21 sec = 0.96 m/s
total displacement = 164.341 m
Explanation:
given data
accelerates = - 2.01 m/s²
time = 7 s
additional time = 6 s
acceleration = +0.518 m/s²
following boat accelerates = 1.49 m/s²
time = 8 s
to find out
velocity of the boat at time 21 s and the total displacement of the boat
solution
we find velocity after 7 second
velocity = accelerate × time
velocity after 7 sec = - 2.01 × 7 = -14.07 m/s
displacement = ut + 0.5 × at²
here u is initial speed = 0 and a is acceleration and t is time
displacement = 0.5 × (-2.01) (7)² = - 49.245 m
and
velocity after (7 + 6) = 13 second is
velocity after 13 sec = -14.07 + ( 6 × 0.518) = -10.96 m/s
displacement = ut + 0.5 × at²
here u is initial speed = -14.07 and a is acceleration and t is time
displacement = -14.07 (6) + 0.5 × (0.518) (6)² = - 75.096 m
and
velocity after (7 + 6 + 8) = 21 second is
velocity after 21 sec = -10.96 + 1.49 × 8 = 0.96 m/s
displacement = -10.96 (8) + 0.5 × (1.49) (8)² = - 40 m
so
total displacement = sum of all displacement
total displacement = (- 49.245) + (- 75.096) + (- 40) = -164.341
total displacement = 164.341 m
(a) The velocity of the boat is 0.958 m/s.
(b) The total displacement of the boat after 21 s is 20.1 m.
Velocity of the boat
The velocity of the boat is determined by using first kinematic equation as shown below;
v = u + at
where;
u is the initial velocity = 0
v = at
∑v = a₁t₁ + a₂t₂ + a₃t₃
v = (-2.01 x 7) + (0.518 x 6) + (1.49 x 8)
v = 0.958 m/s
Total displacement of the boat
The total displacement of the boat after 21 s is calculated as follows;
d = vt
d = 0.958 x 21
d = 20.1 m
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