The time dependence of the path traveled by the body is given by the equation: S = 3 + 2t + t squared.

The time dependence of the path traveled by the body is given by the equation: S = 3 + 2t + t squared. Find the average speed and average acceleration of the body for the first, second and third seconds of its movement.

S (t) = 3 + 2 * t + t ^ 2.

t1 = 1 s.

t2 = 2 s.

t3 = 3 s.

Vav1 -?

acp1 -?

Vcr2 -?

acr2 -?

Vср3 -?

acp3 -?

The average speed of movement Vav and the average acceleration asp are determined by the formulas: Vav = S / t, asp = (V – V0) / t.

Vav1 = S1 / t1, acp1 = (V1 – V0) / t1.

Vav2 = (S2 – S1) / (t2 – t1), asp2 = (V2 – V1) / (t2 – t1).

Vav3 = (S3 – S2) / (t3 – t2), acp3 = (V3 – V2) / (t3 – t2).

S1 = 2 * 1 + (1) ^ 2 = 3 m.

S2 = 2 * 2 + (2) ^ 2 = 8 m.

S3 = 2 * 3 + (3) ^ 2 = 15 m.

Vav1 = 3 m / 1 s = 3 m / s.

Vav2 = (8 m – 3 m) / (2 s – 1 s) = 5 m / s.

Vav3 = (15 m – 8 m) / (3 s – 2 s) = 7 m / s.

According to the dependence of the distance traveled S (t) = 3 + 2 * t + t2, it can be seen that this is a movement with acceleration a = 2 m / s2, initial speed V0 = 2 m / s.

V (t) = V0 + a * t.

V1 = 2 + 2 * 1 = 4 m / s.

V2 = 2 + 2 * 2 = 6 m / s.

V3 = 2 + 2 * 3 = 8 m / s.

acp1 = (V1 – V0) / t1.

arr1 = (4 m / s – 2 m / s) / 1 s = 2 m / s2.

arr2 = (6 m / s – 4 m / s) / 1 s = 2 m / s2.

arr3 = (8 m / s – 6 m / s) / 1 s = 2 m / s2.

Answer: Vav1 = 3 m / s, Vav2 = 5 m / s, Vav3 = 7 m / s, asp1 = asp2 = asp3 = 2 m / s2. – the body moves uniformly accelerated.