(a) In assignments involving one-dimensional motion, when we say acceleration (o

Question

(a) In assignments involving one-dimensional motion, when we say acceleration (or velocity) we are referring to the component of acceleration (or velocity) along the line of motion. This component can be positive, negative or zero. In describing one-dimensional motion, what is the definition of acceleration?


(b) Suppose you had a movie of an object moving along a line and the capability to view it and to acquire and analyze position and velocity data of its motion. How would you go about determining whether or not the object is undergoing a constant acceleration?

A surprising number of motions that we encounter in everyday life involve no acceleration or a constant acceleration. The kinematic equations provide us with a complete mathematical description of any object moving with a constant acceleration if we know its initial position, velocity and acceleration. But not all motions can be described using these equations. For this reason is it important in the study of motion to know how to look at a motion and tell whether or not it involves a constant acceleration. Your task in this assignment is to examine video clips of several objects in motion along a line and determine which objects, if any, are undergoing constant accelerations. The motions you'll study involve a bicycle and rider, two carts moving on separate tracks, and a mass on a small spring. Figure 1: Bicycle and rider Figure 2: A cart with a fan and one without a fan Figure 3: A mass hanging from a spring

Explanation / Answer

1. Acceleration in a given direction is defined as rate of change of velocity along that direction

2. For every successive time intervals calculate: a(t) = ( v(t+dt) - v(t) )/ dt where v(t+dt) = velocity at time t + dt and v(t) = velocity at time t.

If, a(t) comes constant for all time considered, then the object undergoes constant acceleration

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