Question

The position of a particle is given by:

s(t)=t^3+2t^3+5t
t=time
s = distance
Find the acceleration at the relevant time
when the velocity=25 in/sec

Answer 1

To find the acceleration of the particle when the velocity is 25 in/sec, differentiate the given position function twice with respect to time. Then substitute the relevant time into the acceleration function to find the acceleration at that time.

Step-by-step explanation:

To find the acceleration of the particle when the velocity is 25 in/sec, we need to differentiate the given position function, s(t), twice with respect to time.

First, find the velocity function, v(t), by differentiating s(t) with respect to time.

Then, find the acceleration function, a(t), by differentiating v(t) with respect to time. Finally, substitute the relevant time, t, into the acceleration function to find the acceleration at that time.

Example: If s(t) = 3t² , then v(t) = 6t and a(t) = 6. Substituting t=2 into a(t), we get a(2) = 6.

Answer 2

The acceleration at the relevant time when the velocity is 25 in/sec cannot be directly determined without the explicit expression for velocity (v) in terms of time (t).

Step-by-step explanation:

To find acceleration from a position function, it's necessary to derive the velocity function by taking the first derivative of the position function with respect to time (s(t)). Then, the second derivative of the position function (which represents acceleration) can be calculated by differentiating the velocity function with respect to time.

However, without the explicit expression for velocity in terms of time (v(t)), it's impossible to calculate the acceleration directly at a specific velocity value (25 in/sec) since velocity needs to be known as a function of time to find acceleration accurately. To determine acceleration at the given velocity, first, the velocity function needs to be derived from the position function and then equate it to 25 in/sec to find the relevant time(s). After obtaining the time(s), the second derivative of the position function (acceleration) can be evaluated at the identified time(s) to find the acceleration at that particular moment.