NEET Kinematics — Set 13

Question 1

A car moving at $ 60 \, \text{m/s} $ decelerates uniformly to rest over $ 150 \, \text{m} $. What is the time taken to stop?

Accepted Answer

Use $ v^2 = v_0^2 + 2 a x $ to find $ a $: $ 0 = (60)^2 + 2 a (150) \Rightarrow 0 = 3600 + 300 a \Rightarrow a = -12 \, \text{m/s}^2 $. Then, $ v = v_0 + a t $: $ 0 = 60 - 12 t \Rightarrow t = 5 \, \text{s} $. The time taken is $ 5 \, \text{s} $.

Question 2

A stone is dropped from rest. What is its velocity after falling $ 78.4 \, \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 = 78.4 \, \text{m} $. Substitute: $ v^2 = 0 + 2 \cdot 9.8 \cdot 78.4 = 1536.64 \Rightarrow v = \sqrt{1536.64} \approx 39.2 \, \text{m/s} $. The velocity is $ 39.2 \, \text{m/s} $.

Question 3

A cyclist moving at $ 10 \, \text{m/s} $ accelerates at $ 1 \, \text{m/s}^2 $ for $ 5 \, \text{s} $, then decelerates at $ 2 \, \text{m/s}^2 $ to rest. What is the total distance covered?

Accepted Answer

Phase 1: $ v = 10 + 1 \cdot 5 = 15 \, \text{m/s} $, $ x_1 = 10 \cdot 5 + \frac{1}{2} \cdot 1 \cdot (5)^2 = 50 + 12.5 = 62.5 \, \text{m} $. Phase 2: $ t = \frac{15}{2} = 7.5 \, \text{s} $, $ x_2 = 15 \cdot 7.5 - \frac{1}{2} \cdot 2 \cdot (7.5)^2 = 112.5 - 56.25 = 56.25 \, \text{m} $. Total = $ 62.5 + 56.25 = 118.75 \, \text{m} $.

NEET Physics: Kinematics — Practice Set 13

Q1. A car moving at \( 60 \, \text{m/s} \) decelerates uniformly to rest over \( 150 \, \text{m} \). What is the time taken to stop?

Q2. A stone is dropped from rest. What is its velocity after falling \( 78.4 \, \text{m} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q3. A cyclist moving at \( 10 \, \text{m/s} \) accelerates at \( 1 \, \text{m/s}^2 \) for \( 5 \, \text{s} \), then decelerates at \( 2 \, \text{m/s}^2 \) to rest. What is the total distance covered?

Q4. A stone is thrown upwards with a speed of \( 14 \, \text{m/s} \). What is its velocity after \( 1.5 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A body starts from rest and accelerates uniformly at \( 6 \, \text{m/s}^2 \) for \( 3 \, \text{s} \). What is the distance covered?

Q6. A train moving at \( 108 \, \text{km/h} \) decelerates at \( 2 \, \text{m/s}^2 \) for \( 10 \, \text{s} \), then at \( 4 \, \text{m/s}^2 \) until it stops. What is the total time taken to stop?

Q7. A train accelerates uniformly from rest to \( 15 \, \text{m/s} \) over a distance of \( 37.5 \, \text{m} \). What is its acceleration?

Q8. A car moving at \( 27 \, \text{m/s} \) decelerates uniformly to rest in \( 9 \, \text{s} \). What is the distance covered?

Q9. A man running at \( 6 \, \text{m/s} \) throws a ball horizontally at \( 10 \, \text{m/s} \) relative to himself. If it lands \( 12 \, \text{m} \) ahead of the throw point, what is the time of flight? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A particle moves at \( 18 \, \text{m/s} \) and decelerates at \( 4 \, \text{m/s}^2 \) for \( 2 \, \text{s} \), then accelerates at \( 3 \, \text{m/s}^2 \) until its speed is \( 18 \, \text{m/s} \). What is the total distance covered?