What is the velocity of particle independent of time

Question

Assignment:

1. Express the position vector, ??? , in terms of (i) unit vectors, and (ii) magnitude and angle for the two cases below:

(a) Point ?? is located at the coordinate (-3.0,4.0).

(b) Point ?? is located at the coordinate (-1.25,-4.6).

Make certain you express your solutions with the proper # of significant figures.

2. An object's position changes with time according to the graph shown below. For the positions located at Points A, B, C, state whether the velocity is positive, negative, or zero by drawing the tangent lines to the curve and examining their slopes.

(a) At which point is the object moving the slowest?

(b) At which point is the object moving the fastest?

(c) At points A, B, C, state whether the velocity is positive, negative, or zero by drawing the tangent lines to the curve and examining their slopes.

3. The derivative of a polynomial function, tⁿ , is defined as: dtⁿ/dt = nt^n-1

4. The position of a particle at time t is given by x(t) = x₀ + v₀t +1/2at² where x₀,v₀, and a are constants independent of time.

(a) What is the velocity of the particle at time t ?

(b) What is the acceleration of the particle at time t ?

5. The position of a particle moving on the -axis is given by ?? = (6.5??) + (3.7??/??????)?? - (0.2??/??????²)??² with in meters and in seconds.

(a) What is the velocity of the particle at ?? = 2.6 sec?

(b) Is the velocity constant or does it change with time?

The integral of a polynomial function,nt, is defined as:

_ti∫^tf tⁿ dt = tⁿ⁺¹/n+1t_i]t^f = t_fⁿ⁺¹/ n+1 - t_iⁿ⁺¹/n+1

6. The acceleration, ????, of a particle is constant (independent of time).

(a) By integration, show that the velocity of the particle is ??_?? = ??_??0 + ??_???? where ??_??0 is the initial velocity (let ??_?? = ?? and ??_?? = 0, and note that ??_?? = ????/ ???? ).

(b) By integration, find the position of the particle at time t . (let ??_?? = ??, ??_?? = ??₀, ??^?? = ??, and ??_?? = 0)? (Note: the solutions to Part (a) and

(b) are given in the Lecture notes)

7. A particle's acceleration along the ??-axis is ??_?? = 2.3 + 5.2??, with ?? in seconds and ??_?? in meters per second squared.

(a) By integrating, what is the velocity of the particle at time ???

(b) What is the position of the particle at time ???

(c) At ?? = 1.7 sec its velocity is 14 m/sec. What is its velocity at ?? = 4.0?