(C)
Explanation:
The circle has a radius r = 0.5 m, which means that its circumference C is

One revolution means that the stopper travels a distance equal to the circumference of the circle so the velocity of the stopper is

The magnitude of this vector is 15
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.
The magnitude of a vector formula is used to calculate the length for a given vector (say v) and is denoted as |v|. So basically, this quantity is the length between the initial point and endpoint of the vector.
Let vector be = a
component of vector in x direction = 10 i
component of vector in y direction = 10 j
component of vector in z direction = 5 z
vector a = 10 i + 10 j + 5 z
magnitude of vector a = |a| =
= 15
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A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4. f(t) = 12t² + 35 t + 1
Answer:
Velocity = 131 m/s
Speed = 131 m/s
Explanation:
Equation of motion, s = f(t) = 12t² + 35 t + 1
To get velocity of the particle, let us find the first derivative of s
v (t) = ds/dt = 24t + 35
At t = 4
v(4) = 24(4) + 35
v(4) = 131 m/s
Speed is the magnitude of velocity. Since the velocity is already positive, speed is also 131 m/s