Ex 1: The car moves in a straight line such that for a short time its velocity is defined by v = (0.9t2 + 0.6t) m/s where t is in sec. Determine it position and acceleration when t = 3s. When t = 0, s = 0.

Ex 2: A small projectile is forced downward into a fluid medium with an initial velocity of 60m/s. Due to the resistance of the fluid the projectile experiences a deceleration equal to a = (-0.4v3)m/s2, where v is in m/s2. Determine the projectile’s velocity and position 4s after it is fired.

12-6: A freight train travels at v=20(1-e-t) m/s, where t is the elapsed time in seconds. Determine the distance traveled in three seconds, and the acceleration at this time.

12-10: A particle is moving along a straight line such that its acceleration is defined as a=(-2v) m/s2, where v is in meters per second. If v=20 m/s when s=0 and t=0, determine the particle’s velocity as a function of position and the distance the particle moves before it stops.

12-28: The acceleration of a particle along a straight line is defined by a=(2t-9) m/s2, where t is in seconds. At t=0, s=1 m and v=10 m/s. When t=9 s, determine (a) the particle’s position, (b) the total distance traveled and (c) the velocity.

Ex 3: At any instant the horizontal position of the weather balloon is defined by x = (9t) m, where t is in second. If the equation of the path is y = x2/30, determine the distance of the balloon from the station at A, the magnitude and direction of the both the velocity and acceleration when t = 2 s.

Ex 4: The motion of box B is defined by the position vector r = {0.5sin(2t)i + 0.5cos(2t)j – 0.2tk} m, where t is in seconds and the arguments for sine and cosine are in radians (π rad = 180°). Determine the location of box when t = 0.75 s and the magnitude of its velocity and acceleration at this instant.

Ex 5: The chipping machine is designed to eject wood at chips vO = 7.5 m/s. If the tube is oriented at 30° from the horizontal, determine how high, h, the chips strike the pile if they land on the pile 6 m from the tube.

Ex 6: Race car C travels round the horizontal circular track that has a radius of 90 m. If the car increases its speed at a constant rate of 2.1 m/s2, starting from rest, determine the time needed for it to reach an acceleration of 2.4 m/s2. What is its speed at this instant?

12-111: At a given instant the train engine at E has a speed of 20 m/s and an acceleration of 14 m/s2 acting in the direction shown. Determine the rate of increase in the train’s speed and the radius of curvature of the path.

12-125: The two particles A and B start at the origin O and travel in opposite directions along the circular path at constant speeds vA=0.7 m/s and vB=1.5 m/s respectively. Determine at t= 2s, (a) the displacement along the path of each particle, (b) the position vector to each particle, and (c) the shortest distance between the particles.

Ex 7: The rob OA is rotating in the horizontal plane such that θ = (t3) rad. At the same time, the collar B is sliding outwards along OA so that r = (100t2)mm. If in both cases, t is in seconds, determine the velocity and acceleration of the collar when t = 1s.

Ex 8: The searchlight casts a spot of light along the face of a wall that is located 100m from the searchlight. Determine the magnitudes of the velocity and acceleration at which the spot appears to travel across the wall at the instant θ = 45°. The searchlight is rotating at a constant rate of 4 rad/s

12-145: A truck is traveling along the horizontal circular curve of radius r=60 m with a constant speed v=20 m/s. Determine the truck’s radial and transverse components of acceleration

Ex 9: Determine the speed of block A if block B has an upward speed of 2m/s.

12-176: If the hydraulic cylinder at H draws rod BC in by 200 mm, determine how far the slider at A moves.

Ex 10: A man at A s hoisting a safe S by walking to the right with a constant velocity vA = 0.5m/s. Determine the velocity and acceleration of the safe when it reaches the elevation at E. The rope is 30m long and passes over a small pulley at D.

12-181: If block A is moving downward with a speed of 1.2 m/s while C is moving up at 0.6 m/s, determine the speed of block B.

12-187: The cord is attached to the pin at C and passes over the two pulleys at A and D. The pulley at A is attached to the smooth collar that travels along the vertical rod. Determine the velocity of the end of the cord at B if at the instant SA = 1.2 m the collar is moving upwards at 1.5 m/s.

Ex 11: A train, traveling at a constant speed of 90km/h, crosses over a road. If automobile A is traveling t 67.5km/h along the road, determine the magnitude and direction of relative velocity of the train with respect to the automobile.