Question

PLEASE TYPE YOUR ANSWER

Pick and explain in detail one of the following learning goals from Chapter 3 (Motion in Two or Three Dimensions). Additionally, and real life application of the topic you are explaining. (This video should go along with your explanation, and make sure you do not post the same video as someone else)

3.2 (A) - How does one find the vector acceleration of a particle, and why can a particle have acceleration even if its speed is constant?

Answer 1

3.2 (A)

i) Acceleration is the rate of change of the velocity of an object with respect to time. Acceleration is a vector quantity (both magnitude and direction).

Instantaneous acceleration is the first derivative of the velocity vector with respect to time or second derivative of position vector of a particle with respect to time.

ii) A particle can have acceleration even if its speed is constant because acceleration is not rate of change of speed with respect to time but Acceleration is the rate of change of the velocity of a particle with respect to time.So even if only direction of velocity is changing with time , we can have acceleration.

Example- In case of a particle moving in a circular path with constant speed , the direction of instantaneous velocity is along the tangent at the position of the particle at a moment which is always changing.So there is some acceleration in this type of motion.