Calculate the speed of the body in 2 seconds and 5 seconds after the start of movement x = 20 + 2t-t ^ 2.

x (t) = 20 + 2 * t – t ^ 2.

t1 = 2 s.

t2 = 5 s.

V1 -?

V2 -?

The dependence of the speed of movement of the body on time V (t) is the derivative of the dependence of the coordinates of the body on time x (t): V (t) = x (t) “.

V (t) = (20 + 2 * t – t ^ 2) “= 2 – 2 * t.

From the dependence of the speed of movement on time, it can be seen that this is an equally slow motion with an acceleration a = 2 m / s2 and an initial speed V0 = 2 m / s.

V1 (t1) = 2 m / s – 2 m / s2 * 2 s = – 2 m / s.

V2 (t2) = 2 m / s – 2 m / s2 * 5 s = – 8 m / s.

The “-” sign means that the body will move in the opposite direction of the initial movement.

Answer: the body will move in the opposite direction of the initial motion with a speed of V1 = 2 m / s through t1 = 2 s and with a speed of V2 = 8 m / s through t2 = 5 s.