3. A particle starts at rest at point O at instant t=0. The particle accelerates with constant tangential acceleration a_t as it travels along the slit in the direction ccw. Determine r, rdot, theta and thetadot as functions of time during the first revolution of the particle in the slit.

In some applications dealing with very high speeds, the velocity is measured in mm/s. Convert 8mm/s into (a) mis; and (b) mi/h.

Given that P=120lb and Q=130lb, find the rectangular representation of P+Q.

The typical power output of a compact car engine is 110 hp. What is the equivalent power in (a) lbft/s; and (b) kW?

A person weighs 30 lb on the moon, where g=5.32ft/s2. Determine (a) the mass of the person; and (b) the weight of the person on earth.

A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance measured along the beam; [x]=[L] y = displacement of the beam; [y]=[L] = circular frequency of vibration; []=[T1] = mass of the beam per unit length; []=[ML1] D = bending rigidity of beam; [D]=[FL2] Show that the equation is dimensionally homogeneous. Note that [F]=[MLT2] see Eq. (1.21:).

Find the surface area of the 90 duct elbow.

The drag on an airplane wing in flight is known to be a function of the density of air (), the viscosity of air(), the free-stream velocity (U), a characteristic dimension of the wing (s), and the shear stress on the surface of the wing (s). Show that the dimensionless drag, sU2, can be expressed as a function of the Reynolds number, Us.

The three points A(0,2,2),B(1,4,1), and C(3,0,0) define a plane. The coordinates are in inches. Find a unit vector that is perpendicular to this plane.

The length of the position vector r is 240 mm. Determine the rectangular components of (a) r; and (b) the unit vector directed from O toward A.