NEET Kinematics — Set 10

Question 1

A bus moves at a constant speed of $ 36 \, \text{km/h} $ for $ 30 \, \text{minutes} $. What is the distance covered?

Accepted Answer

Convert speed: $ 36 \, \text{km/h} = 36 \cdot \frac{1000}{3600} = 10 \, \text{m/s} $. Time = $ 30 \, \text{min} = 30 \cdot 60 = 1800 \, \text{s} $. Distance $ x = v t = 10 \cdot 1800 = 18000 \, \text{m} = 18 \, \text{km} $. The distance covered is $ 18 \, \text{km} $.

Question 2

A body accelerates uniformly from rest to $ 24 \, \text{m/s} $ over a distance of $ 72 \, \text{m} $. What is the acceleration?

Accepted Answer

Use $ v^2 = v_0^2 + 2 a x $. Here, $ v_0 = 0 $, $ v = 24 \, \text{m/s} $, $ x = 72 \, \text{m} $. Substitute: $ (24)^2 = 0 + 2 a (72) \Rightarrow 576 = 144 a \Rightarrow a = 4 \, \text{m/s}^2 $. The acceleration is $ 4 \, \text{m/s}^2 $.

Question 3

A car moves at $ 16 \, \text{m/s} $ and decelerates at $ 2.5 \, \text{m/s}^2 $ for $ 3 \, \text{s} $, then accelerates at $ 3.5 \, \text{m/s}^2 $ for $ 4 \, \text{s} $. What is the net displacement?

Accepted Answer

Phase 1: $ v = 16 - 2.5 \cdot 3 = 8.5 \, \text{m/s} $, $ x_1 = 16 \cdot 3 - \frac{1}{2} \cdot 2.5 \cdot (3)^2 = 48 - 11.25 = 36.75 \, \text{m} $. Phase 2: $ v = 8.5 + 3.5 \cdot 4 = 22.5 \, \text{m/s} $, $ x_2 = 8.5 \cdot 4 + \frac{1}{2} \cdot 3.5 \cdot (4)^2 = 34 + 28 = 62 \, \text{m} $. Total = $ 36.75 + 62 = 98.75 \, \text{m} $.

NEET Physics: Kinematics — Practice Set 10

Q1. A bus moves at a constant speed of \( 36 \, \text{km/h} \) for \( 30 \, \text{minutes} \). What is the distance covered?

Q2. A body accelerates uniformly from rest to \( 24 \, \text{m/s} \) over a distance of \( 72 \, \text{m} \). What is the acceleration?

Q3. A car moves at \( 16 \, \text{m/s} \) and decelerates at \( 2.5 \, \text{m/s}^2 \) for \( 3 \, \text{s} \), then accelerates at \( 3.5 \, \text{m/s}^2 \) for \( 4 \, \text{s} \). What is the net displacement?

Q4. A rocket accelerates from rest at \( 6 \, \text{m/s}^2 \) for \( 5 \, \text{s} \), then moves at constant speed for \( 3 \, \text{s} \). What is the total distance covered?

Q5. A rocket accelerates vertically at \( 6 \, \text{m/s}^2 \) from rest for \( 4 \, \text{s} \), then its engines fail. What is the maximum height reached above the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A helicopter ascends vertically at \( 6 \, \text{m/s} \) and releases a package after \( 10 \, \text{s} \). How long after release does the package hit the ground if it was initially \( 50 \, \text{m} \) above the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A ball is thrown vertically upwards with an initial speed of \( 15 \, \text{m/s} \). What is the time taken to reach its maximum height? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A particle accelerates uniformly from rest to \( 12 \, \text{m/s} \) in \( 4 \, \text{s} \). What is the distance covered?

Q9. A ball is thrown upwards at \( 30 \, \text{m/s} \) from a \( 40 \, \text{m} \) tower. What is the time taken to reach a point \( 10 \, \text{m} \) above the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A particle starts from rest and moves with a uniform acceleration of \( 3 \, \text{m/s}^2 \) for \( 6 \, \text{s} \). What is the distance covered?