Define the acceleration of an object moving in a straight line.

Verified step by step guidance

1. Understand that acceleration is defined as the rate of change of velocity with respect to time. It can be expressed mathematically as a = rac{dv}{dt}, where 'a' is acceleration, 'dv' is the change in velocity, and 'dt' is the change in time.
2. Recognize that velocity itself is the rate of change of position, which can be expressed as v = rac{dx}{dt}, where 'v' is velocity, 'dx' is the change in position, and 'dt' is the change in time.
3. Identify that if you have a function for position, x(t), you can find velocity by taking the first derivative of this function with respect to time: v(t) = rac{dx(t)}{dt}.
4. To find acceleration, take the derivative of the velocity function: a(t) = rac{dv(t)}{dt} = rac{d^2x(t)}{dt^2}, which gives you the second derivative of the position function with respect to time.
5. Consider the units of acceleration, which are typically expressed in meters per second squared (m/s²), indicating how much the velocity of the object changes per second.