Question

A particle moves along the x-axis so that its velocity at any time t greater than or equal to 0 is given by: v(t)=(2pi-5)t-sin(pi t). Find the acceleration at any time t.

Answer 1

The acceleration function is a(t) = 2π - 5 - π² cos(π t).

Step-by-step explanation:

To find the acceleration of a particle at any time t, given its velocity function v(t), we need to take the derivative of the velocity function with respect to time.

The original velocity function provided is v(t) = (2π - 5)t - π sin(π t).

To calculate the acceleration, we take the derivative of the velocity function:

• The derivative of (2π - 5)t is just 2π - 5 since it is a linear term.
• The derivative of -π sin(π t) with respect to t is -π² cos(π t).

Therefore, the acceleration function is a(t) = 2π - 5 - π² cos(π t).