The movement of a point is given by the equation x = 12t – 2t ^ 2. Determine the average speed

The movement of a point is given by the equation x = 12t – 2t ^ 2. Determine the average speed of the point in the time interval from t1 = 1 s to t2 = 4 s.

x (t) = 12 * t – 2 * t ^ 2.

t1 = 1 s.

t2 = 4 s.

Vav -?

To find the average speed of movement Vav, it is necessary to divide the entire path traveled by point S by the time of its movement t: Vav = S / t.

The path S traversed by the material point is expressed by the formula: S = x2 – x1.

x1 (t1) = 12 * t1 – 2 * t1 ^ 2.

x1 (1 s) = 12 * 1 – 2 * (1) ^ 2 = 10 m.

x2 (t2) = 12 * t2 – 2 * t2 ^ 2.

x2 (4 s) = 12 * 4 = 16 m.

S = 16 m – 10 m = 4 m.

Vav = 4 m / 4 s = 1 m / s.

Answer: the average speed of movement of a material point is Vav = 1 m / s.