Question

the velocity of a particle traveling along an axis is given. near what time is the instantaneous acceleration equal to 0? O t = 0.6 O t = 1 O t = 1.2 O t = 1.6

Answer 1

Without the specific velocity-time relationship, we cannot determine the time when the instantaneous acceleration of a particle is zero.

Step-by-step explanation:

To find the time when the instantaneous acceleration of a particle is equal to zero, we need to look for when the velocity-time graph has a horizontal slope since acceleration is the derivative of velocity with respect to time. Unfortunately, without the specific velocity-time relationship provided in the question, we cannot determine the exact time when the instantaneous acceleration is zero. Normally, if we had a mathematical expression for the velocity v(t), we would find the derivative of the velocity to get a(t), the acceleration as a function of time, and then solve for t when a(t) is zero.

Answer 2

The instantaneous acceleration is equal to 0 near the time t = 1.0 s.

Step-by-step explanation:

To find the time at which the instantaneous acceleration is equal to 0, we need to determine when the particle's acceleration is equal to 0. In this case, the acceleration is given by the second derivative of the position function.

The position function is given as r(t) = (3.0t^2)i + (5.0j) - (6.0t)k.

Taking the second derivative of r(t) with respect to time t, we get a(t) = 6.0i - 6.0k.

Setting a(t) equal to 0 and solving for t, we get:

6.0i - 6.0k = 0

6.0i = 6.0k

i = k

Therefore, near the time when the instantaneous acceleration is equal to 0, t = 1.0 s.