A body of mass m moves rectilinearly under the action of force F = 30H.

A body of mass m moves rectilinearly under the action of force F = 30H. The equation of motion of the body has the form: x: = 6t-4t + 10t ^ 2? m. What is body weight? read the speed after 1 second.

Given:

F = 30 Newton – force acting on a moving body;

x (t) = 6 * t – 4 * t + 10 * t ^ 2 – the equation of body motion;

t = 1 second – time interval.

It is required to determine the body mass m (kilogram) and the body speed after a time interval t (second).

Let’s find the dependence of the speed change on time:

v (t) = x (t) ‘= (6 * t – 4 * t + 10 * t ^ 2)’ = 6 – 4 + 20 * t = 2 + 20 * t.

Let us find the dependence of the change in acceleration on time:

a (t) = v (t) ‘= (2 + 20 * t)’ = 20.

It can be seen that the acceleration is constant and equal to 20 m / s ^ 2.

Then:

m = F / a = 30/20 = 1.5 kilograms.

Let’s substitute the value of t in the equation of dependence of speed on time:

v (t) = 2 + 20 * t = 2 + 20 * 1 = 2 + 20 = 22 m / s.

Answer: body weight is 1.5 kilograms, body speed in 1 second will be 22 m / s.