The body moves according to the law S (t) = t ^ 2 + t Determine at what point in time the speed will be equal to 4.

1. Let’s find the speed of the body by calculating the derivative of the given function of distance from time:

S (t) = t ^ 2 + t;
v (t) = S ‘(t);
v (t) = (t ^ 2 + t) ‘= 2t + 1.
2. Let us determine the moment of time at which the speed of the body reaches the value v0 = 4 m / s:

v (t) = v0;
2t + 1 = 4;
2t = 4 – 1;
2t = 3;
t = 3/2 = 1.5 (s).
Answer: t = 1.5 s.