The equation of motion for a body weighing 2 kg moves according to the law x = 8 + 3t + t ^ 2, determine the momentum of the body in 5 s from the beginning of the movement.
The law x = 8 + 3t + t² almost coincides with the formula for the dependence of the distance traveled on time: x = x₀ + v₀t + at² / 2.
It can be reduced to a form that will allow you to determine the speed and acceleration. It is enough to multiply and divide by 2 the term t²:
x = 8 + 3t + 2t² / 2
The multiplier 3 is the initial velocity v₀, the multiplier 2 in the numerator is the acceleration a.
Speed in 5 s:
v = v₀ + at = 3 + 2 * 5 = 13 m / s.
Body impulse P after 5 s:
P = mv = 2 kg * 13 m / s = 26 kg * m / s
Answer: 26 kg * m / s.
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