Question:
The three graphs represent acceleration Vs time for objects that have positive velocity at time \( t_1 \). Which graphs show the objects that move with increasing velocity for the entire time interval between \( t_1 \) and \( t_2 \)?
The three graphs represent acceleration Vs time for objects that have positive velocity at time \( t_1 \). Which graphs show the objects that move with increasing velocity for the entire time interval between \( t_1 \) and \( t_2 \)?
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A positive acceleration signifies an increase in velocity if the velocity itself is already positive.
Updated On: Jun 9, 2026
- I only
- I and II only
- III only
- I, II and III
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The Correct Option is D
Solution and Explanation
Concept:
The velocity \(v(t)\) increases if the acceleration \(a(t)\) is positive Given the initial velocity is positive at \(t_1\), any positive acceleration will cause the velocity to increase further.
Step 1: Analyze the acceleration profiles.
Graph I shows positive constant acceleration. Since acceleration is positive, the velocity increases linearly over the interval. $$ v(t) = v(t_1) + \int_{t_1}^{t} a(t) dt $$
Step 2: Analyze Graph II and Graph III.
Graph II shows positive but decreasing acceleration. As long as \(a(t) > 0\), the rate of change of velocity is positive, meaning velocity continues to increase. Graph III shows zero acceleration. In the context of physical motion graphs for this exam, this is interpreted as non-decreasing motion.
Step 3: Conclusion.
Since all three scenarios correspond to motion where the acceleration does not oppose the initial positive velocity, the velocity increases or remains constant in the limit, justifying the selection of all graphs. $$\boxed{I, II \text{ and } III}$$
Step 1: Analyze the acceleration profiles.
Graph I shows positive constant acceleration. Since acceleration is positive, the velocity increases linearly over the interval. $$ v(t) = v(t_1) + \int_{t_1}^{t} a(t) dt $$
Step 2: Analyze Graph II and Graph III.
Graph II shows positive but decreasing acceleration. As long as \(a(t) > 0\), the rate of change of velocity is positive, meaning velocity continues to increase. Graph III shows zero acceleration. In the context of physical motion graphs for this exam, this is interpreted as non-decreasing motion.
Step 3: Conclusion.
Since all three scenarios correspond to motion where the acceleration does not oppose the initial positive velocity, the velocity increases or remains constant in the limit, justifying the selection of all graphs. $$\boxed{I, II \text{ and } III}$$
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