Q.22 Which one of the following represents the motion of an object with a positive acceleration?

The motion with positive acceleration is represented by option (C), the velocity–time graph with a straight line sloping upward with time.​

Understanding positive acceleration

• Acceleration is the rate of change of velocity with time: a=ΔvΔta=ΔtΔv.

• On a velocity–time graph, the acceleration equals the slope (gradient) of the line; an upward (positive) slope means positive acceleration, a downward (negative) slope means negative acceleration, and a horizontal line means zero acceleration.​

Option (A): Position vs time, straight line

• In (A), position increases linearly with time, giving a straight line of constant slope on a position–time graph.​

• Constant slope means constant velocity; since velocity is not changing, the acceleration is zero, not positive, so (A) does not represent positive acceleration.​

Option (B): Position vs time, horizontal line

• In (B), the position is constant with time (horizontal line), so the object stays at the same place and its velocity is zero at all times.​

• With velocity remaining zero, there is no change in velocity and therefore the acceleration is also zero, so (B) does not show positive acceleration.​

Option (C): Velocity vs time, line with positive slope

• In (C), the velocity–time graph is a straight line sloping upward as time increases.​

• The positive slope indicates that velocity is increasing with time at a constant rate, which is exactly what positive constant acceleration means, so (C) correctly represents motion with positive acceleration.​

Option (D): Velocity vs time, horizontal line

• In (D), velocity is constant in time (horizontal velocity–time graph), so the slope of the line is zero.​

• Zero slope implies zero acceleration; the object moves with uniform velocity but without speeding up or slowing down, so (D) does not represent positive acceleration.​

Introduction

Understanding the motion of an object with a positive acceleration is essential for mastering basic kinematics and solving conceptual physics questions about graphs. The key idea is that acceleration describes how quickly velocity changes, and this shows up most clearly as the slope of a velocity–time graph. When students can read these graphs correctly, they can instantly recognize whether an object is speeding up, slowing down, or moving with constant velocity.​

Reading position–time graphs

• A position–time graph shows how an object’s position changes over time; the slope of this graph gives the object’s velocity.​

• A straight line with constant slope (like in options A and B) means constant velocity, so the acceleration is zero and the motion of an object with a positive acceleration cannot be represented by such graphs.​

Reading velocity–time graphs

• A velocity–time graph shows how velocity changes with time, and the slope of this graph directly equals the acceleration.​

• A horizontal line (option D) has zero slope and therefore zero acceleration, but a straight line sloping upward (option C) has a positive slope, representing the motion of an object with a positive acceleration.​

Why option (C) is correct

• Positive acceleration means the velocity becomes more positive with time; mathematically, this requires a positive gradient on the velocity–time graph.​

• Option (C) shows this exact situation—a straight, upward‑sloping velocity–time line—so it correctly represents the motion of an object with a positive acceleration, while options (A), (B), and (D) all correspond to zero acceleration.​