NEET Kinematics — Set 9

Question 1

A stone is thrown upwards with a speed of $ 18 \, \text{m/s} $. What is its velocity after $ 2 \, \text{s} $? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Use $ v = v_0 + a t $. Here, $ v_0 = 18 \, \text{m/s} $, $ a = -10 \, \text{m/s}^2 $, $ t = 2 \, \text{s} $. Substitute: $ v = 18 - 10 \cdot 2 = 18 - 20 = -2 \, \text{m/s} $. The velocity is $ -2 \, \text{m/s} $ (downward).

Question 2

A ball is dropped from a height of $ 44.1 \, \text{m} $. What is its velocity just before hitting the ground? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

Use $ v^2 = v_0^2 + 2 g y $. Here, $ v_0 = 0 $, $ g = 9.8 \, \text{m/s}^2 $, $ y = 44.1 \, \text{m} $. Substitute: $ v^2 = 0 + 2 \cdot 9.8 \cdot 44.1 = 864.36 \Rightarrow v = \sqrt{864.36} \approx 29.4 \, \text{m/s} $. The velocity is $ 29.4 \, \text{m/s} $.

Question 3

A stone is dropped from a height $ h $ and falls $ 44.1 \, \text{m} $ in the last $ 1 \, \text{s} $ before hitting the ground. What is the height $ h $? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

Distance in last second: $ d_n = g \cdot \frac{2n - 1}{2} $, $ 44.1 = 9.8 \cdot \frac{2n - 1}{2} \Rightarrow 2n - 1 = 9 \Rightarrow n = 5 \, \text{s} $. Total height: $ h = \frac{1}{2} g t^2 = \frac{1}{2} \cdot 9.8 \cdot (5)^2 = 122.5 \, \text{m} $.

NEET Physics: Kinematics — Practice Set 9

Q1. A stone is thrown upwards with a speed of \( 18 \, \text{m/s} \). What is its velocity after \( 2 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A ball is dropped from a height of \( 44.1 \, \text{m} \). What is its velocity just before hitting the ground? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q3. A stone is dropped from a height \( h \) and falls \( 44.1 \, \text{m} \) in the last \( 1 \, \text{s} \) before hitting the ground. What is the height \( h \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q4. A runner moves at a constant speed of \( 8 \, \text{m/s} \) for \( 25 \, \text{s} \). What is the distance covered by the runner?

Q5. A particle moves at \( 15 \, \text{m/s} \) and decelerates at \( 3 \, \text{m/s}^2 \) for \( 3 \, \text{s} \), then accelerates at \( 2 \, \text{m/s}^2 \) until its speed is \( 15 \, \text{m/s} \). What is the total distance covered?

Q6. A body starts from rest and accelerates at \( 3 \, \text{m/s}^2 \) for \( 4 \, \text{s} \). What is its final velocity?

Q7. A car accelerates uniformly from rest at \( 3 \, \text{m/s}^2 \) for \( 7 \, \text{s} \). What is the final velocity?

Q8. A stone is thrown upwards from a \( 60 \, \text{m} \) cliff at \( 20 \, \text{m/s} \). What is the time taken to reach a point \( 20 \, \text{m} \) below the cliff’s edge? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A train accelerates uniformly from \( 10 \, \text{m/s} \) to \( 30 \, \text{m/s} \) in \( 5 \, \text{s} \). What is its acceleration?

Q10. A car moving at \( 25 \, \text{m/s} \) decelerates uniformly to rest over \( 62.5 \, \text{m} \). What is the time taken to stop?