Motion in a Straight Line | Class 11 Physics Notes

Examples of uniformly accelerated motion

Several examples illustrate the application of kinematic equations for uniformly accelerated motion:

1. Ball thrown vertically upwards from a building (Example 2.3): A ball is thrown upwards with initial velocity v₀ = 20 m/s from a building 25 m high. Taking upward as positive and acceleration due to gravity g = 10 m/s² downward, the maximum height reached and total time before hitting the ground are calculated using kinematic equations.

2. Free fall (Example 2.4): An object falling freely under gravity with acceleration g = 9.8 m/s² downward is described. Starting from rest, its velocity, displacement, and velocity squared as functions of time are given by:

v = -g t,

y = - (1/2) g t²,

v² = -2 g y.

Graphs of acceleration, velocity, and displacement versus time are shown.

3. Galileo's law of odd numbers (Example 2.5): Galileo observed that distances fallen in successive equal time intervals by a freely falling body starting from rest are in the ratio of odd numbers 1:3:5:7... This is demonstrated by calculating distances fallen in successive intervals and showing the ratio matches odd numbers.

4. Stopping distance of vehicles (Example 2.6): When brakes are applied, the stopping distance d_v depends on initial velocity v_it and braking deceleration -α. Using v² = v₀² + 2 a x with final velocity zero, stopping distance is:

d_v = v_it² / (2 α).

This shows stopping distance increases with the square of initial velocity, important for road safety.

5. Reaction time (Example 2.7): Reaction time is the delay between perceiving a situation and responding. It can be measured by dropping a ruler and catching it, then calculating the time taken based on the distance fallen under gravity:

t_r = √(2 d / g).

For a distance d = 21 cm, reaction time is approximately 0.2 s.

📊 Diagram: Fig. 2.6 shows the vertical motion of a ball thrown upwards from a building; Fig. 2.7 shows graphs of acceleration, velocity, and displacement versus time for free fall; Table 2.2 illustrates Galileo's law of odd numbers; Fig. 2.8 shows the ruler drop experiment for reaction time.

🧪 Activity: Measuring reaction time by ruler drop experiment as described in Example 2.7.

🔗 Connection: These examples provide practical applications of kinematic equations, leading to a summary of concepts and definitions in the next section.

Table on page 8 (8×5)