NEET Kinematics — Set 7

Question 1

A particle moves at $ 18 \, \text{m/s} $ and decelerates at $ 3 \, \text{m/s}^2 $ until its speed halves, then accelerates at $ 2 \, \text{m/s}^2 $ to its original speed. What is the total time taken?

Accepted Answer

Phase 1: $ 9 = 18 - 3 t \Rightarrow t_1 = 3 \, \text{s} $. Phase 2: $ 18 = 9 + 2 t \Rightarrow t_2 = 4.5 \, \text{s} $. Total time = $ 3 + 4.5 = 7.5 \, \text{s} $.

Question 2

A rocket accelerates uniformly from rest at $ 8 \, \text{m/s}^2 $ until it reaches a speed of $ 40 \, \text{m/s} $, then maintains that speed for $ 5 \, \text{s} $. What is the total distance covered?

Accepted Answer

Phase 1 (acceleration): $ v = v_0 + a t $, $ 40 = 0 + 8 t \Rightarrow t = 5 \, \text{s} $. Distance: $ x_1 = v_0 t + \frac{1}{2} a t^2 = 0 + \frac{1}{2} \cdot 8 \cdot (5)^2 = 100 \, \text{m} $. Phase 2 (constant speed): $ x_2 = v t = 40 \cdot 5 = 200 \, \text{m} $. Total distance = $ x_1 + x_2 = 100 + 200 = 300 \, \text{m} $.

Question 3

A ball is dropped from a height $ h $ and hits the ground with a speed of $ 29.4 \, \text{m/s} $ after $ 1.5 \, \text{s} $ of fall. What is the value of $ g $ at that location?

Accepted Answer

Use $ v = v_0 + g t $. Here, $ v_0 = 0 $, $ v = 29.4 \, \text{m/s} $, $ t = 1.5 \, \text{s} $. Substitute: $ 29.4 = 0 + g \cdot 1.5 \Rightarrow g = \frac{29.4}{1.5} = 19.6 \, \text{m/s}^2 $. The value of $ g $ is $ 19.6 \, \text{m/s}^2 $.

NEET Physics: Kinematics — Practice Set 7

Q1. A particle moves at \( 18 \, \text{m/s} \) and decelerates at \( 3 \, \text{m/s}^2 \) until its speed halves, then accelerates at \( 2 \, \text{m/s}^2 \) to its original speed. What is the total time taken?

Q2. A rocket accelerates uniformly from rest at \( 8 \, \text{m/s}^2 \) until it reaches a speed of \( 40 \, \text{m/s} \), then maintains that speed for \( 5 \, \text{s} \). What is the total distance covered?

Q3. A ball is dropped from a height \( h \) and hits the ground with a speed of \( 29.4 \, \text{m/s} \) after \( 1.5 \, \text{s} \) of fall. What is the value of \( g \) at that location?

Q4. A bike moving at \( 108 \, \text{km/h} \) comes to rest in \( 9 \, \text{s} \) with uniform deceleration. What is the magnitude of deceleration?

Q5. A car traveling at \( 54 \, \text{km/h} \) comes to rest in \( 10 \, \text{s} \) with uniform deceleration. What is the magnitude of the deceleration?

Q6. A car accelerates from \( 12 \, \text{m/s} \) at \( 1.5 \, \text{m/s}^2 \) for \( 4 \, \text{s} \), then moves at constant speed for \( 5 \, \text{s} \). What is the average speed over the entire motion?

Q7. A stone falls from a height and covers \( 58.8 \, \text{m} \) in the last \( 1.2 \, \text{s} \) of its fall. What is the total height? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q8. A car moves at \( 12 \, \text{m/s} \) and decelerates at \( 2 \, \text{m/s}^2 \) for \( 3 \, \text{s} \), then accelerates at \( 4 \, \text{m/s}^2 \) for \( 4 \, \text{s} \). What is the net displacement?

Q9. A cyclist accelerates from \( 6 \, \text{m/s} \) at \( 1.5 \, \text{m/s}^2 \) for \( 5 \, \text{s} \), then decelerates at \( 2 \, \text{m/s}^2 \) until its speed is \( 8 \, \text{m/s} \). What is the total distance covered?

Q10. A cyclist moves with a constant speed of \( 5 \, \text{m/s} \) for \( 20 \, \text{s} \). What is the distance covered?