Under the action of a force of 200 n, the body moves so that its coordinate in the direction of the action

Under the action of a force of 200 n, the body moves so that its coordinate in the direction of the action of the force changes according to the law x = 25 + 3t + 0.25t. What is its mass?

By definition, acceleration is the second derivative of the law of motion in time, then:

a = x ” (t) = (25 + 3t + 0.25t ^ 2) ” = (3 + 0.5t) ‘= 0.5 m / s ^ 2.

Let’s write Newton’s second law:

F = m * a, where F is force, m is body mass, a is acceleration.

Then:

m = F / a.

Substitute the known values from the condition:

m = 200 / 0.5 = 400 kg.

Answer: the required body weight is 400 kg.