Final answer:
To find the acceleration vector, differentiate the velocity vector with respect to time. Evaluate the velocity and acceleration functions at specified times to find their instantaneous values. Interpreting results involves analyzing the motion through the directions of the acceleration and velocity vectors.
Step-by-step explanation:
To find the normal component of acceleration, you cannot directly use the tangential component; instead, you need to understand the motion of the object in question. If dealing with circular motion, the normal (or centripetal) acceleration can be found using the radius and the tangential (linear) speed. However, the student's question seems to suggest they are working with linear motion, where acceleration has tangential and normal components in a curved path.
To find the functional form of the acceleration, you would:
- Differentiate the velocity vector with respect to time to find the acceleration vector.
To find the instantaneous velocity at given time intervals (like t = 1, 2, 3, and 5 s), follow these steps:
- Evaluate the velocity function V(t) at those specific time values.
Next, to find the instantaneous acceleration at t = 1, 2, 3, and 5 s:
- Evaluate the acceleration function a(t) at those specific times.
Interpreting the results involves comparing the direction of the acceleration and velocity vectors at the specified times and analyzing how the acceleration is affecting the motion of the object.
An example for finding an acceleration vector is:
- Given a velocity of V(t) = 5.0tî + t²ç − 2.0t³ km/s, first differentiate V(t) to find a(t).
- Calculate the acceleration vector at t = 2.0 s and determine its magnitude and direction.