NEET Kinematics — Set 19

Question 1

A stone is dropped from rest. What is the distance covered in the 2nd 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 2nd second, $ n = 2 $. Substitute: $ d = 10 \cdot \frac{2 \cdot 2 - 1}{2} = 10 \cdot \frac{3}{2} = 15 \, \text{m} $. The distance covered is $ 15 \, \text{m} $.

Question 2

A balloon descends at $ 6 \, \text{m/s} $ from $ 100 \, \text{m} $ height and releases a stone $ 2 \, \text{s} $ later. What is the time taken by the stone to hit the ground? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Height at release: $ h = 100 - 6 \cdot 2 = 88 \, \text{m} $. Stone’s initial velocity = $ -6 \, \text{m/s} $. $ -88 = -6 t + \frac{1}{2} \cdot 10 \cdot t^2 \Rightarrow 5 t^2 - 6 t - 88 = 0 $. Solve: $ t = \frac{6 \pm \sqrt{36 + 1760}}{10} = \frac{6 \pm 42.19}{10} $, $ t = 4.82 \, \text{s} $ (positive root).

Question 3

A stone is thrown upwards at $ 15 \, \text{m/s} $ from a tower. It hits the ground $ 4 \, \text{s} $ later. What is the height of the tower? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Use $ y = v_0 t + \frac{1}{2} a t^2 $. Downward is positive, so $ v_0 = -15 \, \text{m/s} $, $ a = 10 \, \text{m/s}^2 $. Substitute: $ y = -15 \cdot 4 + \frac{1}{2} \cdot 10 \cdot (4)^2 = -60 + 80 = 20 \, \text{m} $. Height = $ 20 \, \text{m} $.

NEET Physics: Kinematics — Practice Set 19

Q1. A stone is dropped from rest. What is the distance covered in the 2nd second of its fall? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A balloon descends at \( 6 \, \text{m/s} \) from \( 100 \, \text{m} \) height and releases a stone \( 2 \, \text{s} \) later. What is the time taken by the stone to hit the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A stone is thrown upwards at \( 15 \, \text{m/s} \) from a tower. It hits the ground \( 4 \, \text{s} \) later. What is the height of the tower? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A car moving at \( 50 \, \text{m/s} \) decelerates uniformly to rest over \( 125 \, \text{m} \). What is the time taken to stop?

Q5. A ball is thrown upwards at \( 24 \, \text{m/s} \) from a \( 50 \, \text{m} \) building. How far below the top of the building is it after \( 6 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A rocket is launched vertically at \( 60 \, \text{m/s} \) from the ground. After \( 5 \, \text{s} \), a second rocket is launched at \( 45 \, \text{m/s} \). How long after the second launch do they meet? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A car decelerates uniformly from \( 16 \, \text{m/s} \) to rest over a distance of \( 32 \, \text{m} \). What is the deceleration?

Q8. A vehicle starts from rest and travels \( 50 \, \text{m} \) in \( 5 \, \text{s} \) with uniform acceleration. What is its final velocity?

Q9. A body starts from rest and accelerates uniformly at \( 5 \, \text{m/s}^2 \) for \( 3 \, \text{s} \). What is the distance covered?

Q10. A vehicle moving at \( 30 \, \text{m/s} \) decelerates uniformly to rest in \( 100 \, \text{m} \). What is the time taken to stop?