What is the speed of an object at a given moment
1 answer:
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Answer:
(a) a= 0.139 m/s²
(b) d= 4.45 m
(c) vf= 1.1 m/s
Explanation:
a) We apply Newton's second law:
∑F = m*a Formula (1)
∑F : algebraic sum of the forces in Newton (N)
m : mass (kg)
a : acceleration (m/s²)
Data
F₁= +2.05 * 10³ N : forward push by a motor
F₂= -1.87* 10³ N : resistive force due to the water.
m= 1300 kg
Calculation of the acceleration of the boat
We replace data in the formula (1):
∑F = m*a
F₁+F₂= m*a
a= 0.139 m/s²
b) Kinematics of the boat
Because the boat moves with uniformly accelerated movement we apply the following formulas:
d= v₀t+ (1/2)*a*t² Formula (2)
vf= v₀+at Formula (3)
Where:
d:displacement in meters (m)
t : time interval (s)
v₀: initial speed (m/s)
vf: final speed (m/s)
a: acceleration (m/s² )
Data
v₀ = 0
a= 0.139 m/s²
t = 8 s
Calculation of the distance traveled by the boat in 8 s
We replace data in the formula (2)
d= v₀t+ (1/2)*a*t²
d= 0+ (1/2)*(0.139)*(8)²
d= 4.45 m
c) Calculation of the speed of the boat in 8 s
We replace data in the formula (3):
vf= v₀+at
vf= 0+( 0.139)*(8)
vf= 1.1 m/s