Question

Q No. 1

The position of an object moving along an x axis is given by x = 3t - 4t^2 + t^3, where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object’s displacement between t = 0 and t = 4s? (f)

What is its average velocity for the time interval from t = 2 s to t = 4 s? (g) Graph x versus t for 0 ≤ t ≤4 s and indicate how the answer for (f) can be found on the graph

Question No. 2

A pilot flies horizontally at 1300 km/h, at height h = 35 m above initially level ground. However, at time t = 0, the pilot begins to fly over ground sloping upward at angle θ = 4.3° (Fig). If the pilot does not change the airplane’s heading, at what time t does the plane strike the ground?

Answer 1

1)

a)

$$x = 3(1) - 4(1)^2 + (1)^3=0\ m$$

b)

$$x = 3(2) - 4(2)^2 + (2)^3=-2\ m$$

c)

$$x = 3(3) - 4(3)^2 + (3)^3=0\ m$$

d)

$$x = 3(4) - 4(4)^2 + (4)^3=12\ m$$

e)

$$s=12-0=12\ m$$

f)

$$v=\frac{12-(-2)}{4-2}=7\frac{m}{s}$$

g)

It is the tan of angle between x-axis and line x(2)-x(4).

2)

$$\tan{4.3}=\frac{h}{d}\\\tan{4.3}=\frac{h}{vt}=\frac{35(3.6)}{1300t}\\t=1.29\ s$$