Rectilinear and Curvilinear Motion Practice Quiz (11 questions)

1. Which description correctly characterizes rectilinear motion?

A. Motion along a curved path described with several changing angular parameters

B. Motion along a straight line described with one axis and one position parameter

C. Motion around a fixed point described by an angle and a radius

D. Motion through space described by three independent position parameters

Answer: (B)

Explanation

Rectilinear motion takes place along a straight line, so one axis and one position parameter are sufficient to describe it. Motion along a curved path is curvilinear rather than rectilinear.

2. What distinguishes a particle from a rigid body in describing motion?

A. A particle can translate but has no rotational motion, whereas a rigid body can translate and rotate

B. A particle can rotate but has no translational motion, whereas a rigid body translates without rotation

C. A particle has no mass and remains fixed, whereas a rigid body has mass and changes position

D. A particle translates and rotates as a whole, whereas a rigid body changes shape during motion

Answer: (A)

Explanation

A particle is modeled as an infinitely small object with mass that can undergo translation without rotation. A rigid body may have both translational and rotational motion, making the second choice incorrect.

3. What does the position vector of a point represent?

A. The vector perpendicular to the path, indicating the point's rotational direction

B. The vector from the point back to the origin, indicating its final velocity

C. The vector between two successive positions, indicating how the point moved

D. The vector from the reference-frame origin to the point, indicating its location

Answer: (D)

Explanation

The position vector extends from the reference-frame origin to the point and specifies its location. A vector between two positions represents displacement rather than position.

4. A particle has positions $x(t_1)=3\ \text{m}$ and $x(t_2)=11\ \text{m}$ along a straight axis. What is its displacement between these times?

A. $8\ \text{m}$ in the positive direction

B. $3\ \text{m}$ in the positive direction

C. $14\ \text{m}$ in the positive direction

D. $8\ \text{m}$ in the negative direction

Answer: (A)

Explanation

Displacement is calculated as final position minus initial position, so $\Delta x=x(t_2)-x(t_1)=11\ \text{m}-3\ \text{m}=8\ \text{m}$ in the positive direction. Adding the two positions would give a distance from the origin rather than the displacement.

5. What does average velocity represent for a particle moving along a straight line?

A. The magnitude of the instantaneous velocity vector

B. The displacement divided by the elapsed time

C. The instantaneous slope of the position–time curve

D. The total distance divided by the elapsed time

Answer: (B)

Explanation

Average velocity is defined as displacement divided by elapsed time, so it includes directional information through the sign of the displacement. Average speed instead uses total distance, while the other two descriptions refer to instantaneous quantities.

6. For a particle moving in one dimension, how is instantaneous acceleration defined mathematically?

A. As the first derivative of position with respect to time

B. As the second derivative of position with respect to time

C. As displacement divided by elapsed time

D. As the total distance divided by elapsed time

Answer: (B)

Explanation

Instantaneous acceleration is the rate of change of velocity, equivalently the second derivative of position with respect to time. The first derivative of position describes instantaneous velocity, not acceleration.

7. What is the role of integrating acceleration over a time interval in constant-acceleration motion?

A. It determines the particle’s initial position at the start

B. It determines the change in velocity during that interval

C. It determines the acceleration at the interval’s midpoint

D. It determines the distance traveled without using velocity

Answer: (B)

Explanation

Integrating acceleration with respect to time gives the change in velocity, represented by the area under the acceleration–time curve. The particle’s initial position is instead an initial condition, while distance and midpoint acceleration require different information or calculations.

8. Near Earth’s surface, what acceleration does an object experience during free fall when air resistance is neglected?

A. A downward acceleration of approximately $9.81\,\mathrm{m\,s^{-2}}$

B. An acceleration of approximately $9.81\,\mathrm{m\,s^{-1}}$ directed horizontally

C. A downward acceleration that increases with the object’s mass

D. An upward acceleration of approximately $9.81\,\mathrm{m\,s^{-2}}$

Answer: (A)

Explanation

In ideal free fall near Earth’s surface, gravity gives every object the same downward acceleration of about $9.81\,\mathrm{m\,s^{-2}}$, independent of mass. The mass-dependent choice is incorrect because gravitational acceleration is the same for objects when air resistance is absent.

9. How do instantaneous velocity and instantaneous speed differ for a particle following a curved trajectory?

A. Velocity is a scalar derivative of distance, whereas speed is a vector derivative of position

B. Velocity measures total path length, whereas speed measures displacement along the trajectory

C. Velocity is tangent to the trajectory and can have direction, whereas speed is its positive magnitude

D. Velocity points toward the center of curvature, whereas speed gives the radial component

Answer: (C)

Explanation

Instantaneous velocity is a vector tangent to the trajectory, while instantaneous speed is the positive magnitude of that vector, computed from its components. The path-length and displacement definitions describe average speed and average velocity rather than their instantaneous curvilinear counterparts.

10. Why does a projectile’s horizontal velocity remain constant when air resistance is neglected?

A. Its total acceleration becomes zero after the projectile is launched

B. Its horizontal velocity decreases because gravity opposes the launch

C. Its horizontal acceleration is zero because gravity acts vertically

D. Its vertical acceleration is zero because gravity acts horizontally

Answer: (C)

Explanation

Gravity contributes acceleration in the vertical direction, so the projectile has zero horizontal acceleration and retains a constant horizontal velocity. The option claiming that gravity acts horizontally reverses the direction of gravitational acceleration.

11. A motion sensor tracks a small object whose path remains a straight line. Which mathematical description is appropriate for analyzing its motion?

A. Use three axes and three angles to describe the object’s rotation

B. Use one axis and one position coordinate to describe the motion

C. Use two independent axes to describe its curved trajectory

D. Use a full rigid-body model to track its orientation changes

Answer: (B)

Explanation

Rectilinear motion occurs along a straight line, so one axis and one position parameter are sufficient to describe the particle’s translation. A three-dimensional or rigid-body description would introduce variables that are not needed for this one-dimensional motion.