If the law of motion has the form x = 5t + 3t ^ 2. Then the initial velocity of the body is equal to.

Initial data: the law of motion of the body x = 5t + 3t ^ 2.

Method 1) Define the law of change in the speed of a body (we take the first-order derivative): V = S ‘= x’ = (5t + 3t ^ 2) ‘= 5 * 1 + 2 * 3 * t = 5 + 6t.

Let’s calculate the initial speed at time t = 0 s: V0 = 5 + 6 * 0 = 5 m / s.

Method 2) Comparison with the formula for calculating the distance traveled: S = V0 * t + a * t ^ 2/2, whence V0 = 5 m / s, a = 6 m / s2.

Answer: The initial velocity of the body is 5 m / s.