Question

A particle moves along a line so that at time t, where 0 ≤ t ≤ π, its position is given by s(t)=−4cost−t²​/2+10. What is the velocity of the particle when its acceleration is zero? (A) -5.19 (B) 0.74 (C) 1.32 (D) 2.55 (E) 8.13

Answer 1

To find the velocity when the acceleration is zero, the time at which the acceleration is zero needs to be determined, using the differentiation of the velocity function with respect to time. Substituting the time when acceleration is zero into the velocity function will yield the velocity. The position function, velocity function, and acceleration function can be derived from the given information.

Step-by-step explanation:

The velocity of a particle can be found by differentiating the position function with respect to time. The acceleration of the particle can be found by differentiating the velocity function with respect to time. When the acceleration is zero, it means that the velocity is constant. Therefore, to find the velocity when the acceleration is zero, we need to find the time at which the acceleration is zero and substitute this time into the velocity function.

The position function is given as s(t) = -4cos(t) - t^2/2 + 10.

Now, to find when the acceleration is zero, we need to differentiate the velocity function with respect to time:

a(t) = -4sin(t) - 1

To find the time at which the acceleration is zero, we set the acceleration function equal to zero:

-4sin(t) - 1 = 0

-4sin(t) = 1

sin(t) = -1/4

t = 7π/6 or 11π/6 (since 0 ≤ t ≤ π)

Substituting t = 7π/6 or t = 11π/6 into the velocity function v(t) = ds/dt, we can find the velocity when the acceleration is zero.