NEET Kinematics — Set 8

Question 1

Two stones are dropped from a height of $ 125 \, \text{m} $, with a $ 2 \, \text{s} $ interval between them. How far apart are they when the second stone has fallen for $ 3 \, \text{s} $? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Stone 1 (after 5 s): $ y_1 = \frac{1}{2} \cdot 10 \cdot (5)^2 = 125 \, \text{m} $ (hits ground). Stone 2 (after 3 s): $ y_2 = \frac{1}{2} \cdot 10 \cdot (3)^2 = 45 \, \text{m} $. Distance apart = $ 125 - 45 = 80 \, \text{m} $.

Question 2

A stone falls freely from rest and reaches a velocity of $ 14.7 \, \text{m/s} $. How long did it fall? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

Use $ v = v_0 + g t $. Here, $ v_0 = 0 $, $ v = 14.7 \, \text{m/s} $, $ g = 9.8 \, \text{m/s}^2 $. Substitute: $ 14.7 = 0 + 9.8 t \Rightarrow t = \frac{14.7}{9.8} = 1.5 \, \text{s} $. The time of fall is $ 1.5 \, \text{s} $.

Question 3

A ball is dropped from rest. What is the distance covered in the 3rd second of its fall? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Distance in $ n $-th second = $ g \cdot \frac{2n - 1}{2} $. For 3rd second, $ n = 3 $. Substitute: $ d = 10 \cdot \frac{2 \cdot 3 - 1}{2} = 10 \cdot \frac{5}{2} = 25 \, \text{m} $. The distance covered is $ 25 \, \text{m} $.

NEET Physics: Kinematics — Practice Set 8

Q1. Two stones are dropped from a height of \( 125 \, \text{m} \), with a \( 2 \, \text{s} \) interval between them. How far apart are they when the second stone has fallen for \( 3 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A stone falls freely from rest and reaches a velocity of \( 14.7 \, \text{m/s} \). How long did it fall? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q3. A ball is dropped from rest. What is the distance covered in the 3rd second of its fall? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. Two stones are dropped from a height of \( 80 \, \text{m} \), \( 1.5 \, \text{s} \) apart. How long after the second stone is released do they meet if the first rebounds at \( 15 \, \text{m/s} \) upon hitting the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A bike accelerates uniformly from rest to \( 20 \, \text{m/s} \) over a distance of \( 40 \, \text{m} \). What is its acceleration?

Q6. A stone is dropped from a height of \( 45 \, \text{m} \) on a planet where it takes \( 3 \, \text{s} \) to reach the ground. What is the acceleration due to gravity on this planet?

Q7. A train moving at \( 72 \, \text{km/h} \) passes a pole in \( 9 \, \text{s} \). If it decelerates uniformly to rest in \( 30 \, \text{s} \) after passing the pole, what is the length of the train?

Q8. A rocket ascends with an acceleration of \( 4 \, \text{m/s}^2 \) for \( 6 \, \text{s} \), then its engines shut off. How long does it take to reach its maximum height from the start? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A stone is thrown upwards at \( 30 \, \text{m/s} \) from a \( 55 \, \text{m} \) tower. How far below the tower’s top is it after \( 7 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A ball is thrown upwards with a speed of \( 38 \, \text{m/s} \). What is its velocity after \( 3 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2 \))