An object oscillates along a vertical line, and its position i...

Question

An object oscillates along a vertical line, and its position in centimeters is given by y(t) = 30(sint - 1), where t ≥ 0 is measured in seconds and y is positive in the upward direction.

Find the velocity of the oscillator, v(t) =y′(t).

Accepted Answer

Welcome back, everyone. A wave travels along a string and its position in a millimeters as described by H of T equals 15 multiplied by T cosine of T + 1 for T greater than or equal to 0, where T represents time in seconds. Determine the velocity of the wave V of T equals H T. And where are given 4 answer choices A says V of T equals 30 st millimeters per second. B says ne30 st millimeters per second, C 15 squad of tim per second, and D 30 cos squaret millimeters per second. So let's consider the given function. It says H of T equals 15, multiplied by T cosine of T + 1. According to the context of the problem, we want to evaluate the velocity function, which is the first derivative of H, right? So we want to differentiate it. We're going to use the factor constant. And then in prints we're going to not consider the two, right? We can factor it out. We simply want to differentiate cosine of T and then we want to differentiate 1, which is a constant, and we have to recall that the derivative of cosine is equal to negative sign. So essentially we're going to use this definition for our differentiation. So V of T would be equal to 15 multiplied by. Now the derivative of cosine is negative sign, we get -2 st plus 0 because the derivative of 1 is 0, that's a constant. So now we can simplify we're going to get -30s T. What about the units? Well, essentially we know that. The position is given in millimeters, right? And now the first derivative represents the rate of change, so we're going to get position per unit time, right, and our time is represented in seconds. So our final answer would be negative 30 st millimeters per second, which corresponds to the answer choice B. Thank you for watching.

An object oscillates along a vertical line, and its position in centimeters is given by y(t) = 30(sint - 1), where t ≥ 0 is measured in seconds and y is positive in the upward direction.​Find the velocity of the oscillator, v(t) =y′(t).

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An object oscillates along a vertical line, and its position in centimeters is given by y(t) = 30(sint - 1), where t ≥ 0 is measured in seconds and y is positive in the upward direction.
Find the velocity of the oscillator, v(t) =y′(t).