NEET Kinematics — Set 15

Question 1

A stone falls from a height of $ 98 \, \text{m} $ on a planet and takes $ 3.5 \, \text{s} $ to reach the ground. What is the gravitational acceleration on this planet?

Accepted Answer

$ h = \frac{1}{2} g t^2 $, $ 98 = \frac{1}{2} g (3.5)^2 \Rightarrow 98 = 6.125 g \Rightarrow g = 16 \, \text{m/s}^2 $.

Question 2

A ball is thrown upwards at $ 28 \, \text{m/s} $ from the ground. At the same instant, another ball is dropped from $ 80 \, \text{m} $ above. Where do they meet relative to the ground? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Ball 1: $ y_1 = 28 t - 5 t^2 $. Ball 2: $ y_2 = 80 - 5 t^2 $. Meet when $ y_1 = y_2 $: $ 28 t - 5 t^2 = 80 - 5 t^2 \Rightarrow 28 t = 80 \Rightarrow t = \frac{20}{7} \approx 2.86 \, \text{s} $. Height: $ y_1 = 28 \cdot \frac{20}{7} - 5 \cdot \left(\frac{20}{7}\right)^2 = 80 - 5 \cdot \frac{400}{49} = 80 - 40.82 = 39.18 \, \text{m} $.

Question 3

A ball is thrown upwards at $ 20 \, \text{m/s} $ from a $ 50 \, \text{m} $ tower. What is its speed when it passes $ 20 \, \text{m} $ below the tower’s top? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Displacement $ y = -20 \, \text{m} $, $ v^2 = (20)^2 + 2 \cdot 10 \cdot 20 = 400 + 400 = 800 $. $ v = \sqrt{800} \approx 28.28 \, \text{m/s} $.

NEET Physics: Kinematics — Practice Set 15

Q1. A stone falls from a height of \( 98 \, \text{m} \) on a planet and takes \( 3.5 \, \text{s} \) to reach the ground. What is the gravitational acceleration on this planet?

Q2. A ball is thrown upwards at \( 28 \, \text{m/s} \) from the ground. At the same instant, another ball is dropped from \( 80 \, \text{m} \) above. Where do they meet relative to the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A ball is thrown upwards at \( 20 \, \text{m/s} \) from a \( 50 \, \text{m} \) tower. What is its speed when it passes \( 20 \, \text{m} \) below the tower’s top? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A runner moving at \( 7 \, \text{m/s} \) throws a ball horizontally at \( 14 \, \text{m/s} \) relative to himself. If it lands \( 21 \, \text{m} \) ahead of the throw point, what is the time of flight? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A bus starts from rest and moves with a uniform acceleration of \( 1.5 \, \text{m/s}^2 \) for \( 8 \, \text{s} \). What is the final velocity of the bus?

Q6. A truck moving at \( 15 \, \text{m/s} \) decelerates uniformly and stops after \( 30 \, \text{m} \). How long does it take to stop?

Q7. A stone falls from a height and covers \( 68.6 \, \text{m} \) in the last \( 1.5 \, \text{s} \) of its fall. What is the total height? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q8. A person walks \( 8 \, \text{m} \) in \( 2 \, \text{s} \) and then walks back \( 4 \, \text{m} \) in \( 1 \, \text{s} \). What is the average speed?

Q9. A particle moves at \( 12 \, \text{m/s} \) and decelerates at \( 3 \, \text{m/s}^2 \) for \( 2 \, \text{s} \), then accelerates at \( 4 \, \text{m/s}^2 \) until it regains \( 12 \, \text{m/s} \). What is the total distance covered?

Q10. A train accelerates uniformly from \( 8 \, \text{m/s} \) to \( 20 \, \text{m/s} \) in \( 6 \, \text{s} \). What is the distance covered?