Graph slopes and areas Knowledge-Based Practice

Questions

1. 1.

   Two cars start from the same position at $t = 0$ and travel in the positive direction along a straight path. Car 1 moves with a constant speed, while Car 2 starts from rest and accelerates uniformly until their velocity-versus-time graphs intersect at time $t_1$. At time $t_1$, which statement correctly compares their positions?

   • A) Car 2 is ahead of Car 1 because it is accelerating throughout the interval.
   • B) Both cars are at the same position because their velocity-versus-time graphs intersect at that instant.
   • C) Car 1 is ahead of Car 2 because the area under its velocity-versus-time graph is twice as large.
   • D) Both cars are at the same position because they have identical speeds at that instant.
2. 2.

   An object moves along a straight line during a time interval from $t_1$ to $t_2$. If the net area enclosed between its velocity-versus-time graph and the time axis over this interval is zero, which statement must be true?

   • A) The object remained stationary throughout the entire time interval.
   • B) The total distance traveled by the object over the time interval is zero.
   • C) The object has the same position at time $t_2$ as it had at time $t_1$.
   • D) The acceleration of the object was zero throughout the entire time interval.
3. 3.

   An object moves along a straight line with a constant negative acceleration. Which graph representing this motion is a straight line with a constant negative slope?

   • A) Position-versus-time graph
   • B) Acceleration-versus-time graph
   • C) Speed-versus-time graph
   • D) Velocity-versus-time graph
4. 4.

   An object moves along a straight line. Which feature of its position-versus-time graph indicates that the object is reversing its direction of motion?

   • A) The graph crosses the time axis.
   • B) The slope of the graph changes algebraic sign.
   • C) The slope of the graph remains constant and non-zero.
   • D) The concavity of the graph changes from upward to downward.
5. 5.

   For an object moving along a straight line, what physical quantity is obtained by dividing the net area bounded by its velocity-versus-time graph and the time axis over a time interval by the duration of that interval?

   • A) The average velocity over the interval
   • B) The average acceleration over the interval
   • C) The average speed over the interval
   • D) The instantaneous velocity at the midpoint of the interval
6. 6.

   For an object moving along a straight line, what physical quantity is represented by the slope of a secant line connecting two points at times $t_1$ and $t_2$ on its position-versus-time graph?

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

   An object moves along a straight line such that its position-versus-time graph has a constant, non-zero slope throughout a time interval. What is the slope of its velocity-versus-time graph during this interval?

   • A) A non-zero constant equal to the velocity of the object
   • B) Zero
   • C) A non-zero constant equal to the displacement of the object
   • D) Continuously increasing over time
8. 8.

   At a given instant, an object moving along a straight line has a negative slope on its position-versus-time graph and a positive slope on its velocity-versus-time graph. Which statement correctly describes the object's motion at that instant?

   • A) The object is moving in the negative direction and slowing down.
   • B) The object is moving in the negative direction and speeding up.
   • C) The object is moving in the positive direction and speeding up.
   • D) The object is moving in the positive direction and slowing down.
9. 9.

   An object moves along a straight line such that its position-versus-time graph is concave downward throughout a time interval. What does this concavity indicate about the object's acceleration during this interval?

   • A) The acceleration is negative.
   • B) The acceleration is positive.
   • C) The acceleration is zero.
   • D) The acceleration is constantly increasing.
10. 10.

    An object moves along a straight line. If the tangent line to its position-versus-time graph is horizontal at time $t_1$, what can be concluded about the object's motion at that instant?

    • A) The object's acceleration is zero.
    • B) The object's position coordinate is zero.
    • C) The object is moving with a constant non-zero speed.
    • D) The object's instantaneous velocity is zero.
11. 11.

    An object moves along a straight line such that, over a given time interval, the area bounded by its velocity-versus-time graph and the time axis is 15 m above the axis and 6 m below the axis. What are the displacement and the total distance traveled by the object during this interval?

    • A) Displacement of 9 m and total distance of 21 m
    • B) Displacement of 21 m and total distance of 9 m
    • C) Displacement of 9 m and total distance of 9 m
    • D) Displacement of 21 m and total distance of 21 m
12. 12.

    A linear velocity-versus-time graph for a particle moving along a straight line passes through the coordinates (2 s, 14 m/s) and (6 s, 2 m/s). Based on the slope of this graph, what is the acceleration of the particle?

    • A) 3 m/s²
    • B) -3 m/s²
    • C) -2 m/s²
    • D) 4 m/s²
13. 13.

    An object moves along a straight line as its velocity decreases uniformly from 16 m/s to 4 m/s over a time interval of 5 s. Based on the area bounded by its velocity-versus-time graph and the time axis, what is the displacement of the object during this interval?

    • A) 20 m
    • B) 30 m
    • C) 50 m
    • D) 80 m
14. 14.

    An object moves along a straight line with an initial velocity of -4 m/s at t = 0. If the area bounded by its acceleration-versus-time graph and the time axis between t = 0 and t = 6 s is +18 m/s, what is the velocity of the object at t = 6 s?

    • A) +18 m/s
    • B) +22 m/s
    • C) +14 m/s
    • D) +3 m/s
15. 15.

    For an object moving in one dimension, which physical quantity is directly determined by the slope of the tangent line to its position-versus-time graph at a specific instant?

    • A) Instantaneous acceleration
    • B) Total displacement
    • C) Instantaneous velocity
    • D) Average acceleration
16. 16.

    For an object moving along a straight line, what physical quantity is represented by the net area bounded by the velocity-versus-time graph and the time axis over a given time interval?

    • A) Average acceleration
    • B) Total distance traveled
    • C) Displacement
    • D) Instantaneous acceleration
17. 17.

    For an object moving along a straight line, which pair correctly identifies the physical quantity represented by the slope of its velocity-versus-time graph and the area bounded by its acceleration-versus-time graph and the time axis, respectively?

    • A) Acceleration and change in velocity
    • B) Change in velocity and acceleration
    • C) Acceleration and total displacement
    • D) Displacement and change in velocity

Answers and step-by-step solutions appear after you finish the test.