v (t) = 3 + 4 * t – the equation of the dependence of the speed of a material point on time.
It is required to determine the initial velocity of a material point v0 (meter per second) and the modulus of its acceleration a (m / s2).
To determine the initial speed of a material point, you need to substitute the value t = 0 (initial moment of time) in the equation of the speed dependence:
v0 = 3 + 4 * 0 = 3 + 0 = 3 meters per second.
To find the acceleration, you need to perform the first-degree derivative of the velocity equation:
a = v (t) ‘= (3 + 4 * t)’ = 4 m / s2.
Answer: initial speed is 3 m / s, acceleration is 4 m / s2.
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