At the instant shown, cars A and B travel at speeds of 70 mi / h and 50 mi / h, respectively. If B is increasing its speed by $1100 mi / h ^2$, while A maintains a constant speed, determine the velocity and acceleration of B with respect to A. Car B moves along a curve having a radius of curvature of 0.7 mi.

A beam is loaded and supported as shown in figure. Use singularity functions to find the deflection (a) At the right end of the beam. (b) At a section midway between the supports.

Crates A and B weigh 100 lb and 50 lb, respectively. If they start from rest, determine their speed when t = 5 s. Also, find the force exerted by crate A on crate B during the motion. The coefficient of kinetic friction between the crates and the ground is $\mu_k = 0.25$.

The rotating nozzle sprays a large circular area and turns with the constant angular rate $\dot{\theta}=K$. Particles of water move along the tube at the constant rate $i=c$ relative to the tube. Write expressions for the magnitudes of the velocity and acceleration of a water particle $P$ for a given position $l$ in the rotating tube.

The boats A and B travel with constant speeds of $v_A=15 \mathrm{~m} / \mathrm{s}$ and $v_B=10 \mathrm{~m} / \mathrm{s}$ when they leave the pier at O at the same time. Determine the distance between them when t=4 s.

The car A is ascending a parking-garage ramp in the form of a cylindrical helix of 24-ft radius rising 10 ft for each half turn.The car has a speed of 15 mi/hr, which is decreasing at the rate of 2 mi/hr per second. Determine the r-, $\theta$- and z-components of the acceleration of the car.

Find the acceleration of an 800-kg car that has a net force of 4,000 N acting upon it.

If end A of the rope moves downward with a speed of 5 m/s, determine the speed of cylinder B.

Car $A$ starts from rest at $t=0$ and travels along a straight road with a constant acceleration of $6 \mathrm{ft} / \mathrm{s}^2$ until it reaches a speed of $80 \mathrm{ft} / \mathrm{s}$. Afterwards it maintains this speed. Also, when $t=0$, car $B$ located $6000 \mathrm{ft}$ down the road is traveling towards $A$ at a constant speed of $60 \mathrm{ft} / \mathrm{s}$. Determine the distance traveled by car $A$ when they pass each other.

Determine the smallest radius that should be used for a highway if the normal component of the acceleration of a car traveling at 72 km/h is not to exceed 0.8 $m/s^2$.

Determine the speed of the elevator if each motor draws in the cable with a constant speed of 5m/s.

Locate the centroid of the shaded area given below.

A spiral transition curve is used on railroads to connect a straight portion of the track with a curved portion. If the spiral is defined by the equation $y=\left(10^{-6}\right) x^3$, where $x$ and $y$ are in feet, determine the magnitude of the acceleration of a train engine moving with a constant speed of $40 \mathrm{ft} / \mathrm{s}$ when it is at point $x=600 \mathrm{ft}$.

The car travels along the circular curve having a radius r=400 ft. At the instant shown, its angular rate of rotation is $\dot{\theta}=0.025 \mathrm{rad} / \mathrm{s}$, which is decreasing at the rate $\ddot{\theta}=-0.008 \mathrm{rad} / \mathrm{s}^2$. Determine the radial and transverse components of the car's velocity and acceleration at this instant and sketch these components on the curve.