The movement of the car is given by the equation: x (t) = 15t + t ^ 2. What is the mass of the machine
| June 9, 2021 | education
The movement of the car is given by the equation: x (t) = 15t + t ^ 2. What is the mass of the machine if the resultant force applied to the machine is 3kN.
x (t) = 15 * t + t ^ 2.
F = 3 kN = 3000 N.
m -?
According to 2 Newton’s law, the mass of a body m is equal to the ratio of the resultant force F to the acceleration of the body a: m = F / a.
The dependence of the acceleration of the body on time a (t) is the derivative of the dependence of the speed of motion on time V (t) “or the second derivative of the dependence of the coordinate on time: a (t) = V (t)” = x (t) “”.
V (t) = x (t) “= (15 * t + t ^ 2) = 15 + 2 * t.
a (t) = V (t) “= (5 + 2 * t) = 2 m / s2.
m = 3000 N / 2 m / s2 = 1500 kg.
Answer: the body has a mass m = 1500 kg.
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