Motion in a Straight Line | Class 11 Physics Notes

2.3 Acceleration

Acceleration describes how the velocity of an object changes with time. Historically, there was debate whether velocity changes should be described with respect to time or distance. Galileo's studies of free-falling bodies and motion on inclined planes showed that the rate of change of velocity with time is constant for free fall, leading to the concept of acceleration as the rate of change of velocity with time.

Average acceleration over a time interval Δt is defined as the change in velocity Δv divided by Δt:

average acceleration ā = (v₂ - v₁) / (t₂ - t₁) = Δv / Δt

Instantaneous acceleration a at a time t is the limit of average acceleration as Δt → 0:

a = lim (Δt → 0) (Δv / Δt) = dv/dt

Acceleration is a vector quantity and can be positive, negative, or zero. It can result from changes in the magnitude of velocity (speed), direction of velocity, or both. For example, acceleration can be positive if velocity increases in the positive direction, or negative if velocity decreases or direction reverses.

Velocity-time graphs illustrate acceleration. The slope of the velocity-time curve at any instant gives instantaneous acceleration. For constant acceleration, the velocity-time graph is a straight line. The area under the velocity-time graph between two times gives the displacement during that interval.

Examples of velocity-time graphs for constant acceleration include: (a) Positive velocity with positive acceleration (velocity increases). (b) Positive velocity with negative acceleration (velocity decreases). (c) Negative velocity with negative acceleration (velocity magnitude increases in negative direction). (d) Velocity changing direction due to negative acceleration.

Position-time graphs for motion with positive, negative, and zero acceleration show characteristic shapes: upward curve (parabola) for positive acceleration, downward curve for negative acceleration, and straight line for zero acceleration.

In this chapter, the focus is on motion with constant acceleration, where average acceleration equals instantaneous acceleration throughout the motion.

📊 Diagram: Fig. 2.3 Velocity-time graph for motions with constant acceleration. (a) Motion in positive direction with positive acceleration, (b) Motion in positive direction with negative acceleration, (c) Motion in negative direction with negative acceleration, (d) Motion of an object with negative acceleration that changes direction at time t₁. Between times 0 to t₁, it moves in positive x-direction and between t₁ and t₂ it moves in the opposite direction.

🔗 Connection: This section prepares for deriving kinematic equations for motion with uniform acceleration in the next section.