NEET Kinematics — Set 18

Question 1

A car decelerates uniformly from $ 25 \, \text{m/s} $ to rest over a distance of $ 62.5 \, \text{m} $. What is the deceleration?

Accepted Answer

Use $ v^2 = v_0^2 + 2 a x $. Here, $ v = 0 $, $ v_0 = 25 \, \text{m/s} $, $ x = 62.5 \, \text{m} $. Substitute: $ 0 = (25)^2 + 2 a (62.5) \Rightarrow 0 = 625 + 125 a \Rightarrow a = -5 \, \text{m/s}^2 $. Magnitude of deceleration is $ 5 \, \text{m/s}^2 $.

Question 2

A stone is dropped from a height of $ 122.5 \, \text{m} $. How long does it take to reach the ground? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

For free fall, use $ y = \frac{1}{2} g t^2 $. Here, $ y = 122.5 \, \text{m} $, $ g = 10 \, \text{m/s}^2 $. Substitute: $ 122.5 = \frac{1}{2} \cdot 10 \cdot t^2 \Rightarrow 122.5 = 5 t^2 \Rightarrow t^2 = 24.5 \Rightarrow t = \sqrt{24.5} \approx 4.95 \, \text{s} $. Rounded to one decimal, the time is $ 5 \, \text{s} $.

Question 3

A ball is thrown vertically upwards with a speed of $ 30 \, \text{m/s} $. What is the maximum height reached? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Use $ v^2 = v_0^2 + 2 a h $. At max height, $ v = 0 $, $ v_0 = 30 \, \text{m/s} $, $ a = -10 \, \text{m/s}^2 $. Substitute: $ 0 = (30)^2 + 2 (-10) h \Rightarrow 0 = 900 - 20 h \Rightarrow h = \frac{900}{20} = 45 \, \text{m} $. The maximum height is $ 45 \, \text{m} $.

NEET Physics: Kinematics — Practice Set 18

Q1. A car decelerates uniformly from \( 25 \, \text{m/s} \) to rest over a distance of \( 62.5 \, \text{m} \). What is the deceleration?

Q2. A stone is dropped from a height of \( 122.5 \, \text{m} \). How long does it take to reach the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A ball is thrown vertically upwards with a speed of \( 30 \, \text{m/s} \). What is the maximum height reached? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A runner starts from rest and accelerates at \( 1.5 \, \text{m/s}^2 \) for \( 4 \, \text{s} \), then maintains constant speed. What is the average speed over the first \( 10 \, \text{s} \)?

Q5. A body accelerates uniformly from rest to \( 22 \, \text{m/s} \) over a distance of \( 121 \, \text{m} \). What is the acceleration?

Q6. A stone is dropped from rest. What is the distance covered in the 7th second of its fall? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A ball is thrown vertically upwards with a speed of \( 35 \, \text{m/s} \). What is the time taken to reach the maximum height? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A runner moving at \( 5 \, \text{m/s} \) throws a ball horizontally at \( 15 \, \text{m/s} \) relative to himself. If it lands \( 18 \, \text{m} \) ahead of the throw point, what is the time of flight? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A projectile is launched vertically at \( 50 \, \text{m/s} \) from the ground. After \( 6 \, \text{s} \), a second projectile is launched at \( 40 \, \text{m/s} \). When do they meet? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A ball is thrown upwards with a speed of \( 50 \, \text{m/s} \). How long does it take to return to the ground? (Take \( g = 10 \, \text{m/s}^2 \))