Question

For the position of a particle moving along the x-axis given by x(t) = ..., what is the acceleration of the particle at the point where the velocity is first equal to 0?

a) 2t
b) 6t
c) 12t
d) 24t

Answer 1

To find the acceleration when velocity is zero, we would typically differentiate the velocity function to get acceleration, solve the velocity function for time when it's zero, and substitute that time back into the acceleration function. Unfortunately, the complete position or velocity function is not provided in the question, so we cannot perform the calculation.

Step-by-step explanation:

The question involves finding the acceleration of a particle at a point in time when its velocity is first equal to zero. To find the acceleration at the moment when velocity is zero, we can utilize the given velocity function and differentiate it with respect to time to obtain the acceleration as a function of time. Then, we can solve the velocity equation for when it equals zero to find the specific time at which this occurs. Once we have that time, we substitute it back into the acceleration function to get the acceleration at that instant.

However, without the complete velocity function provided in the question, we cannot give a precise numeric answer. Typically, for a position function of the form x(t) = at + bt2 + c, the velocity function would be v(t) = a + 2bt, and the acceleration would be the constant 2b. But since the exact position function is not specified in this instance, we cannot proceed with the calculation.