Question

How to find the tangential component of acceleration with T (tangent)?

a) Differentiate the velocity vector
b) Differentiate the position vector
c) Integrate the velocity vector
d) Integrate the position vector

Answer 1

To find the tangential component of acceleration, differentiate the velocity vector with respect to time and identify the component in the direction of the velocity.

Step-by-step explanation:

To find the tangential component of acceleration, we apply option (a) and differentiate the velocity vector. By taking the first derivative of the velocity vector with respect to time, we get the acceleration vector, which can be resolved into tangential and normal (or radial) components.

The tangential acceleration is the component of acceleration that is tangent to the path of a moving object, and it represents the rate at which the object's speed along the path changes. The steps to find this component include:

1. Find the functional form of the acceleration by differentiating the velocity function with respect to time.
2. Identify and separate the tangential component of this acceleration vector, which is in the direction of the velocity vector.

For a particle with velocity V(t) = 5.0tî + t²ç - 2.0t³ km/s, you would calculate its acceleration vector by differentiating each component of V(t) with respect to time.