CHAPTER 2 KINEMATICS OF PARTICLES

What is the branch of dynamics that describes the motion of bodies without reference to the forces that cause the motion?

The position coordinate of a particle moving in a straight line is given by s = 2t^3 - 24t + 6, where s is in meters and t is in seconds. What is the acceleration of the particle when its velocity is 30 m/s?

In the graphical analysis of rectilinear motion, what physical quantity does the area under the velocity-time (v-t) curve between two time points, t1 and t2, represent?

A particle moves along a straight line with a constant acceleration. If it starts with an initial velocity of 2 m/s and reaches a velocity of 10 m/s over a distance of 24 m, what is its acceleration?

According to the principles of plane curvilinear motion, which statement about the instantaneous velocity vector is always true?

A projectile is launched with an initial velocity of 200 m/s at an angle of 60 degrees above the horizontal. Neglecting air resistance, what is the vertical component of its velocity after 5 seconds? Use g = 9.81 m/s^2.

For a particle moving along a curved path, the normal component of acceleration, an, is always directed toward what point?

A car is traveling at a constant speed of 30 m/s around a circular track with a radius of 300 m. What is the magnitude of its acceleration?

In polar coordinates (r-theta), what does the term r*(d(theta)/dt) represent?

A particle's motion is described by the polar coordinates r = 4t meters and theta = 0.5t radians. What is the magnitude of its radial velocity (vr) at t = 2 seconds?

In the analysis of relative motion with translating axes, if vA is the absolute velocity of particle A, vB is the absolute velocity of particle B, and vA/B is the velocity of A relative to B, what is the correct vector relationship between them?

An aircraft A is flying east at a constant velocity of 400 km/h. A second aircraft B is flying north at a constant velocity of 300 km/h. What is the magnitude of the velocity of aircraft B as observed from aircraft A (vB/A)?

What does it mean for a system of connected particles to have 'one degree of freedom'?

In the pulley system shown in Figure 2/19, a block A moves horizontally, connected by a cable to a pulley holding a vertically moving block B. What is the relationship between the horizontal velocity of A (vA) and the vertical velocity of B (vB)?

When describing motion in three dimensions, which coordinate system adds a z-coordinate and its time derivatives to the polar-coordinate description of plane motion?

A particle moves with a velocity v and an acceleration a. If the tangential component of its acceleration, at, is zero, what can be concluded about the particle's motion?

What is the key distinction between constrained and unconstrained motion?

An engineering student is analyzing projectile motion. For a first treatment, which of the following is NOT a standard assumption?

In rectilinear motion, the acceleration of a particle is given by a = 3v, where v is the velocity in m/s. If the particle starts at v = 2 m/s at t = 0, which integral would be used to find the time when the velocity is 4 m/s?

What is the mathematical definition of the instantaneous acceleration vector, a?

The position of a particle in plane curvilinear motion is given by the vector r = (3t^2)i + (4t)j meters. What is the magnitude of its acceleration at t = 2 seconds?

In the n-t coordinate system, the total acceleration vector 'a' is the vector sum of which two components?

A race car increases its speed uniformly from 50 m/s to 70 m/s as it goes around a circular curve of 400 m radius. At the instant its speed is 60 m/s, what is the magnitude of its total acceleration?

A car travels on a curved road. It has a constant tangential deceleration of 2 m/s^2. At the instant its speed is 25 m/s, the radius of curvature of the road is 125 m. What is the magnitude of its total acceleration at this instant?

The time derivatives of the unit vectors in polar coordinates, er and e_theta, are non-zero because the vectors change in which property?

What is the primary method for analyzing the motion of interconnected particles, such as those in a pulley system?

A car accelerates from rest in a straight line. Its acceleration is given by a = 4 - 0.1s, where 's' is the distance in meters. What is its velocity when it has traveled 20 meters?

If a particle moves in a circle of constant radius 'r', how do the polar coordinate velocity components (vr, v_theta) relate to the speed v?

A particle has a velocity vector v = 3i + 4j and an acceleration vector a = 6i - 8j. Which of the following statements is true?

An aircraft B appears to be moving away from an observer in aircraft A at a 60-degree angle from A's line of flight. Aircraft A is flying east at 800 km/h. Aircraft B is actually heading 45 degrees north of east. What is the true speed of aircraft B?

What does the term 'hodograph' refer to in the context of kinematics?

A particle's acceleration is constant at a = 2i - 3j m/s^2. If its initial velocity at t=0 was v0 = 10i + 15j m/s, what is its velocity vector v at t = 4s?

A ball is thrown from the top of a 100 m tall building with a horizontal velocity of 20 m/s. How far horizontally from the base of the building does the ball land? Neglect air resistance and use g = 9.81 m/s^2.

What is the radius of curvature (ρ) of a particle's path at a point where the particle is momentarily at rest (v=0)?

In the analysis of a system with two degrees of freedom, like the pulley system in Figure 2/20, what is the key feature of the relationship between the velocities of the bodies A, B, and C?

A particle moves along the x-axis with an acceleration a = -kx, where k is a positive constant. This type of motion is characteristic of what physical system?

For a particle in circular motion with radius r, its acceleration components in polar coordinates are ar = -r*(theta_dot)^2 and a_theta = r*(theta_double_dot). How does the radial acceleration 'ar' relate to the normal acceleration 'an'?

An observer in Car B, which is rounding a curve, measures the acceleration of Car A. Why must the reference axes attached to Car B be non-rotating for the standard relative acceleration equation (aA = aB + aA/B) to be valid?

The velocity of a particle is given by v = 2t^2 - 8t m/s. At which time(s) is the particle momentarily at rest?

What is the key difference between the vector displacement (delta r) and the scalar distance traveled (delta s) for a particle in curvilinear motion?

A particle moves along a straight line with its position given by s = t^3 - 6t^2 + 5 meters. What is its total distance traveled in the first 5 seconds?

A particle moves along a straight line with its position given by s = t^3 - 6t^2 + 5 meters. What is its total distance traveled in the first 5 seconds?

In the graphical interpretation of rectilinear motion, what does the slope of the velocity vs. position (v-s) graph at a point represent?

An aircraft pulls into a steep 45-degree climb at 300 km/h. At this moment, it releases a package. What are the initial horizontal and vertical components of the package's velocity? (Use standard x-y axes).

The acceleration vector of a particle is given by a = -r*(theta_dot)^2 * er + r*(theta_double_dot) * e_theta. This expression is for which coordinate system and which type of motion?

A block A has a rightward velocity of 2 m/s. It is connected by a cable and pulley system to block B. For every 1 meter block A moves to the right, block B moves down by 0.5 meters. What is the velocity of block B?

In space curvilinear motion, what coordinate system uses one radial distance (R) and two angles (theta and phi) to specify a particle's position?

If car A has an acceleration of aA = 2i m/s^2 and car B has an acceleration of aB = 3j m/s^2, what is the acceleration of A relative to B (aA/B)?

At the apex (highest point) of a projectile's trajectory, which component of velocity is momentarily zero?

A particle moves in a circular path of radius 5 m. At a certain instant, its speed is 10 m/s and its tangential acceleration is 4 m/s^2. What is the magnitude of its total acceleration at this instant?