11.3.A.1Multiple Choice
A car's motion is described as: "starts at rest, speeds up steadily for 5 s, then travels at constant speed." Which velocity-vs-time graph correctly represents this motion?
Select A, B, C, or D to check your answer.
Directions: Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions mix the five essential knowledge threads of Topic 1.3 — representing motion in multiple forms, the three constant-acceleration kinematic equations, free fall near Earth's surface, reading velocity and acceleration as slopes on motion graphs, and reading displacement and change in velocity as areas under motion graphs. Use g = 10 m/s² unless a problem states otherwise, and round decimals to the nearest tenth.
A car's motion is described as: "starts at rest, speeds up steadily for 5 s, then travels at constant speed." Which velocity-vs-time graph correctly represents this motion?
Select A, B, C, or D to check your answer.
Describe, in words, the motion represented by an x-t graph that starts at the origin, curves upward with increasing slope for 3 s, then becomes a straight line with constant (nonzero) slope afterward.
An object's motion is given by the equation x(t) = 2 + 3t (meters, t in seconds). Which narrative best describes this motion?
Select A, B, C, or D to check your answer.
A ball is dropped from rest and falls under gravity. Represent this motion three ways: (a) a brief narrative description, (b) a word-equation relating velocity to time, (c) a qualitative description of the shape of its v-t graph.
A problem gives an object's initial velocity, its constant acceleration, and the time elapsed, and asks for its displacement. Which kinematic equation is most directly suited to this problem?
Select A, B, C, or D to check your answer.
A car starts from rest and accelerates at 4 m/s² for 5 s. (a) Find its velocity at t = 5 s. (b) Find its displacement during those 5 s.
A ball's velocity increases from 0 to 30 m/s while it travels 90 m under constant acceleration. The time this takes is not given. What is its acceleration?
Select A, B, C, or D to check your answer.
Explain why the equation v_x² = v_0x² + 2a_x(x − x₀) is especially useful in problems where time is not given, and verify algebraically that it contains no t.
An object is dropped from rest near Earth's surface (ignore air resistance). Which statement correctly describes its acceleration as it falls?
Select A, B, C, or D to check your answer.
A rock is dropped from rest from a cliff and takes 3 s to hit the ground. Taking downward as positive and g = 10 m/s², (a) find its velocity just before impact, and (b) find the height of the cliff.
A ball is thrown straight upward and returns to the thrower's hand. Taking upward as positive (so aₓ = −g), which statement is correct about its velocity and acceleration at the very top of its path?
Select A, B, C, or D to check your answer.
Explain why, when solving a free-fall problem, the sign you assign to g depends on which direction you chose as positive — and why the magnitude (≈10 m/s²) never changes.
On a position-vs-time graph, the slope of the tangent line at a particular instant gives...
Select A, B, C, or D to check your answer.
A position-vs-time graph is a horizontal line for the first 2 s, then becomes a straight line with positive slope for the next 3 s. (a) Describe the object's velocity during each part. (b) Is the object accelerating during either part? Explain.
On a velocity-vs-time graph, the slope of the tangent line at a particular instant gives...
Select A, B, C, or D to check your answer.
A velocity-vs-time graph is a straight line with slope −4 m/s² for the first 3 s, then slope 0 for the next 2 s. The velocity starts positive and stays positive throughout. (a) Find the acceleration during each part. (b) Describe what's physically happening to the object's speed during each part.
A v-t graph shows a constant velocity of 6 m/s for 4 s. What is the object's displacement during this interval?
Select A, B, C, or D to check your answer.
A v-t graph is a straight line that increases linearly from 0 m/s to 20 m/s over 4 s (constant acceleration). (a) Find the displacement during this interval using the area under the v-t graph. (b) Verify your answer using the kinematic equation x = x₀ + v₀t + ½at².
An a-t graph shows a constant acceleration of 3 m/s² for 5 s, then zero for the next 2 s. What is the total change in velocity over the full 7 s?
Select A, B, C, or D to check your answer.
An a-t graph shows acceleration of +4 m/s² for the first 2 s, then −2 m/s² for the next 4 s. (a) Find the change in velocity during the first 2 s. (b) Find the change in velocity during the next 4 s. (c) Find the object's total change in velocity over the full 6 s, and its final velocity if it started at rest.