NEET Kinematics — Set 16

Question 1

Two stones are released from a height of $ 98 \, \text{m} $, $ 1 \, \text{s} $ apart. How long after the second stone is released do they meet? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

Stone 1: $ y_1 = \frac{1}{2} \cdot 9.8 \cdot (t + 1)^2 $. Stone 2: $ y_2 = \frac{1}{2} \cdot 9.8 \cdot t^2 $. Meet when $ y_1 = y_2 $: $ 4.9 (t + 1)^2 = 98 \Rightarrow (t + 1)^2 = 20 \Rightarrow t + 1 = 4.47 \Rightarrow t = 3.47 \, \text{s} $. Relative: $ y_1 - y_2 = 98 \Rightarrow 4.9 (t^2 + 2t + 1 - t^2) = 98 \Rightarrow 9.8 t + 4.9 = 98 \Rightarrow t = 9.5 \, \text{s} $ (error, use total height). Correct: They meet when first hits ground, $ t = 4.47 - 1 = 3.47 \, \text{s} $.

Question 2

A ball is thrown upwards at $ 40 \, \text{m/s} $ from a $ 25 \, \text{m} $ tower. What is the time taken to hit the ground? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

$ y = v_0 t - \frac{1}{2} g t^2 $, $ y = -25 $, $ v_0 = 40 \, \text{m/s} $. $ -25 = 40 t - 5 t^2 \Rightarrow 5 t^2 - 40 t - 25 = 0 \Rightarrow t^2 - 8 t - 5 = 0 $. Solve: $ t = \frac{8 \pm \sqrt{64 + 20}}{2} = \frac{8 \pm 9.17}{2} $, $ t = 8.585 \, \text{s} $ (positive root).

Question 3

A ball is thrown vertically upwards with a speed of $ 24 \, \text{m/s} $. What is the total time of flight? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Time to max height: $ v = v_0 + a t $, $ 0 = 24 - 10 t \Rightarrow t = 2.4 \, \text{s} $. Total time = time up + time down = $ 2.4 \, \text{s} + 2.4 \, \text{s} = 4.8 \, \text{s} $. The total time is $ 4.8 \, \text{s} $.

NEET Physics: Kinematics — Practice Set 16

Q1. Two stones are released from a height of \( 98 \, \text{m} \), \( 1 \, \text{s} \) apart. How long after the second stone is released do they meet? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q2. A ball is thrown upwards at \( 40 \, \text{m/s} \) from a \( 25 \, \text{m} \) tower. What is the time taken to hit the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A ball is thrown vertically upwards with a speed of \( 24 \, \text{m/s} \). What is the total time of flight? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A stone falls freely from a height of \( 78.4 \, \text{m} \). How long does it take to reach the ground? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q5. A cyclist accelerates from \( 8 \, \text{m/s} \) at \( 2 \, \text{m/s}^2 \) for \( 4 \, \text{s} \), then decelerates at \( 3 \, \text{m/s}^2 \) to \( 10 \, \text{m/s} \). What is the total distance covered?

Q6. A motorcycle accelerates uniformly from rest at \( 2.5 \, \text{m/s}^2 \) for \( 6 \, \text{s} \). What is the final velocity?

Q7. A body accelerates uniformly from rest to a velocity of \( 20 \, \text{m/s} \) over a distance of \( 50 \, \text{m} \). What is the acceleration?

Q8. A stone falls freely from a height of \( 98 \, \text{m} \). How long does it take to reach the ground? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q9. A stone is thrown upwards at \( 35 \, \text{m/s} \) from a \( 45 \, \text{m} \) cliff. How far below the cliff’s edge is it after \( 8 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A train moving at \( 126 \, \text{km/h} \) decelerates at \( 2 \, \text{m/s}^2 \) for \( 10 \, \text{s} \), then at \( 5 \, \text{m/s}^2 \) until it stops. What is the total distance covered during deceleration?