NEET Kinematics — Set 3

Question 1

A car accelerates uniformly from $ 10 \, \text{m/s} $ to $ 30 \, \text{m/s} $ over a distance of $ 80 \, \text{m} $. What is the acceleration?

Accepted Answer

Use $ v^2 = v_0^2 + 2 a x $. Here, $ v = 30 \, \text{m/s} $, $ v_0 = 10 \, \text{m/s} $, $ x = 80 \, \text{m} $. Substitute: $ (30)^2 = (10)^2 + 2 a (80) \Rightarrow 900 = 100 + 160 a \Rightarrow 160 a = 800 \Rightarrow a = 5 \, \text{m/s}^2 $. The acceleration is $ 5 \, \text{m/s}^2 $.

Question 2

A cyclist moves at a constant speed of $ 15 \, \text{km/h} $ for $ 12 \, \text{minutes} $. What is the distance covered?

Accepted Answer

Convert speed: $ 15 \, \text{km/h} = 15 \cdot \frac{1000}{3600} = \frac{25}{6} \, \text{m/s} $. Time = $ 12 \, \text{min} = 12 \cdot 60 = 720 \, \text{s} $. Distance $ x = v t = \frac{25}{6} \cdot 720 = 3000 \, \text{m} = 3 \, \text{km} $. The distance covered is $ 3 \, \text{km} $.

Question 3

An object falls freely from rest. What is its velocity after traveling $ 4.9 \, \text{m} $? (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 = 4.9 \, \text{m} $. Substitute: $ v^2 = 0 + 2 \cdot 9.8 \cdot 4.9 = 96.04 \Rightarrow v = \sqrt{96.04} \approx 9.8 \, \text{m/s} $. The velocity is $ 9.8 \, \text{m/s} $.

NEET Physics: Kinematics — Practice Set 3

Q1. A car accelerates uniformly from \( 10 \, \text{m/s} \) to \( 30 \, \text{m/s} \) over a distance of \( 80 \, \text{m} \). What is the acceleration?

Q2. A cyclist moves at a constant speed of \( 15 \, \text{km/h} \) for \( 12 \, \text{minutes} \). What is the distance covered?

Q3. An object falls freely from rest. What is its velocity after traveling \( 4.9 \, \text{m} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q4. A balloon descends at \( 5 \, \text{m/s} \) from \( 150 \, \text{m} \) and releases a stone after \( 3 \, \text{s} \). What is the time taken by the stone to hit the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A body moving with an initial velocity of \( 20 \, \text{m/s} \) comes to rest after traveling \( 40 \, \text{m} \) under uniform retardation. What is the magnitude of its acceleration?

Q6. A cyclist accelerates from \( 10 \, \text{m/s} \) at \( 2 \, \text{m/s}^2 \) for \( 3 \, \text{s} \), then decelerates at \( 1.5 \, \text{m/s}^2 \) until its speed is \( 12 \, \text{m/s} \). What is the total distance covered?

Q7. A stone is dropped from a height of \( 125 \, \text{m} \). What is its velocity just before hitting the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A car accelerates from rest at \( 4 \, \text{m/s}^2 \) for \( 6 \, \text{s} \), then decelerates at \( 3 \, \text{m/s}^2 \) until its speed is \( 12 \, \text{m/s} \). What is the total distance covered?

Q9. A stone falls from a height of \( 80 \, \text{m} \) on a planet and takes \( 4 \, \text{s} \) to reach the ground. What is the gravitational acceleration on this planet?

Q10. A ball is thrown upwards with a speed of \( 36 \, \text{m/s} \). What is the maximum height reached? (Take \( g = 10 \, \text{m/s}^2 \))

Q11. A ball is thrown upwards at \( 50 \, \text{m/s} \) from a cliff. It returns to the cliff’s height after \( 12 \, \text{s} \). What is the height of the cliff? (Take \( g = 10 \, \text{m/s}^2 \))

Q12. A train accelerates from rest at \( 2 \, \text{m/s}^2 \) for \( 10 \, \text{s} \), then decelerates at \( 1 \, \text{m/s}^2 \) to rest. What is the total distance covered?

Q13. Two balls are dropped from a height of \( 180 \, \text{m} \), with a \( 1.5 \, \text{s} \) interval. What is their separation when the first ball hits the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q14. A person walks \( 10 \, \text{m} \) in \( 4 \, \text{s} \) and then walks back \( 2 \, \text{m} \) in \( 1 \, \text{s} \). What is the average speed?

Q15. A train accelerates uniformly from rest to \( 10 \, \text{m/s} \) over a distance of \( 25 \, \text{m} \). What is the acceleration?