The equation of motion of a material point has the form x = 0.4 – t ^ 2 (m).

The equation of motion of a material point has the form x = 0.4 – t ^ 2 (m). Write down the dependence formula V (t) and build its graph. Calculate the distance traveled in 4 s.

To find the dependence of the speed of a point on time, it is necessary to differentiate the dependence of its coordinate on time:

v (t) = ds (t) / dt;

v (t) = (0.4 – t ^ 2) ‘= -2t.

The graph v (t) is a straight line passing through the points (0; 0) and (1; -2).

To find the path traversed in the first 4 s of motion, it is necessary to take a definite integral of v (t) with the limits of integration 0 and 4:

Int from 0 to 4 (-2t * dt) = 0 ^ 2 – (-4 ^ 2) = 16 m.