Velocity–time graphs Knowledge-Based Download PDF

Questions

1. 1.

   Which of the following procedures correctly determines the average velocity of an object over a given time interval directly from its velocity–time graph?

   • A) Calculating the slope of the secant line connecting the initial and final points of the interval
   • B) Taking the arithmetic mean of the initial and final instantaneous velocities
   • C) Reading the value of the instantaneous velocity at the midpoint of the time interval
   • D) Dividing the net area bounded by the graph and the time axis by the duration of the time interval
2. 2.

   Which of the following physical quantities cannot be determined solely from an object's velocity–time graph without specifying an initial condition?

   • A) The instantaneous acceleration at any specific time
   • B) The total displacement over a chosen time interval
   • C) The exact position of the object at a specific instant
   • D) The direction of motion of the object at any instant
3. 3.

   An object moves along a straight line such that its velocity–time graph is a smooth curve. If the tangent to the curve is horizontal at a specific instant, which of the following statements must be true at that instant?

   • A) The object has momentarily come to rest.
   • B) The instantaneous acceleration of the object is zero.
   • C) The net displacement of the object is zero.
   • D) The object reverses its direction of motion.
4. 4.

   On a velocity–time graph of an object moving along a straight line, what does it indicate about the motion of the object whenever the plotted line approaches the time axis?

   • A) The object is moving toward its initial position.
   • B) The object is slowing down.
   • C) The object is speeding up in the negative direction.
   • D) The magnitude of the object's acceleration is decreasing.
5. 5.

   If the velocity–time graphs of two objects moving along the same straight line intersect at time $t$, which of the following statements must be true at that instant?

   • A) Both objects are located at the same position.
   • B) Both objects have the same instantaneous velocity.
   • C) Both objects experience the same instantaneous acceleration.
   • D) Both objects have undergone the same total displacement.
6. 6.

   On a velocity–time graph for an object moving along a straight line, what quantity is represented by the slope of a secant line connecting two points at times $t_1$ and $t_2$?

   • A) The instantaneous acceleration at time $t_1$
   • B) The average velocity over the time interval from $t_1$ to $t_2$
   • C) The average acceleration over the time interval from $t_1$ to $t_2$
   • D) The total displacement over the time interval from $t_1$ to $t_2$
7. 7.

   Over a given time interval, the net signed area bounded by an object's velocity–time graph and the time axis is equal to zero. Which of the following statements must be true regarding the object's motion during this interval?

   • A) The total distance traveled by the object during the interval is zero.
   • B) The final position of the object is identical to its initial position.
   • C) The object remained stationary throughout the entire interval.
   • D) The average acceleration of the object over the interval is zero.
8. 8.

   A car moves along a straight path such that its velocity–time graph is a curve whose slope continuously becomes steeper over time. What does this graph indicate about the motion of the car?

   • A) Its acceleration is increasing over time.
   • B) Its acceleration is constant and non-zero.
   • C) Its acceleration is decreasing over time.
   • D) Its acceleration is zero throughout the motion.
9. 9.

   An object moves along a straight line such that its velocity–time graph is a straight line sloping downward from +20 m/s to +5 m/s over a given time interval. Which statement correctly describes the motion of the object during this interval?

   • A) It moves in the positive direction with a decreasing speed and a constant negative acceleration.
   • B) It moves in the negative direction with an increasing speed and a constant negative acceleration.
   • C) It moves in the positive direction with an increasing speed and a constant positive acceleration.
   • D) It moves in the negative direction with a decreasing speed and a constant positive acceleration.
10. 10.

    Which of the following statements correctly describes the motion of an object whose velocity–time graph is a horizontal line situated below the time axis?

    • A) The object remains at rest at a fixed position in the negative coordinate region.
    • B) The object moves with a constant speed in the negative reference direction.
    • C) The object slows down at a constant rate while moving in the negative direction.
    • D) The object accelerates uniformly in the positive reference direction.
11. 11.

    Which characteristic of a velocity–time graph indicates that an object moving along a straight line has reversed its direction of motion?

    • A) The slope of the graph changes from positive to negative.
    • B) The graph reaches an extremum where its slope is temporarily zero.
    • C) The net area enclosed between the curve and the time axis equals zero.
    • D) The curve crosses the horizontal time axis from one side to the other.
12. 12.

    A velocity–time graph for an object moving along a straight line features a horizontal segment at 8 m/s from t = 0 to t = 4 s, followed by a straight line decreasing to 0 m/s at t = 10 s. What is the total displacement of the object during this 10 s interval?

    • A) 40 m
    • B) 48 m
    • C) 56 m
    • D) 80 m
13. 13.

    A body moves along a straight line such that its velocity decreases uniformly from +12 m/s to -6 m/s over a time interval of 6 s. What is the total distance traveled by the body during this 6 s interval?

    • A) 18 m
    • B) 30 m
    • C) 36 m
    • D) 42 m
14. 14.

    On a velocity–time graph, an object moving in a straight line increases its velocity uniformly from 4 m/s to 16 m/s over a time interval of 6 s. What are the magnitude of the acceleration and the displacement of the object during this interval?

    • A) 1.5 m/s² and 72 m
    • B) 2 m/s² and 120 m
    • C) 2 m/s² and 60 m
    • D) 3 m/s² and 48 m