Make up the equation of motion and calculate the path traversed

Make up the equation of motion and calculate the path traversed by the body in 10 s, if the speed depends on time according to the law v = 3t ^ {2}.

Given:

v (t) = 3 * t ^ 2 – dependence of speed on time;

t = 10 seconds.

It is required to draw up an equation of body motion and find the path traversed in time t.

Let’s find the initial speed:

v (0) = 3 * 0 ^ 2 = 0 m / s.

the equation of the dependence of speed on time in the general case looks like this:

v (t) = v0 + a * t;

3 * t ^ 2 = a * t;

a = 3 * t.

Then, the equation of motion will have the form:

S = a * t ^ 2/2 = 3 * t ^ 3/2

In 10 seconds, the body will cover the distance:

S = 3 * 10 ^ 3/2 = 3 * 1000/2 = 3 * 500 = 1500 meters.

Answer: in 10 seconds the body will cover a path equal to 1500 meters.