NEET Kinematics — Set 11

Question 1

A rocket accelerates from rest at $ 5 \, \text{m/s}^2 $ for $ 8 \, \text{s} $, then moves at constant speed for $ 4 \, \text{s} $. What is the total distance covered?

Accepted Answer

Phase 1: $ v = 5 \cdot 8 = 40 \, \text{m/s} $, $ x_1 = \frac{1}{2} \cdot 5 \cdot (8)^2 = 160 \, \text{m} $. Phase 2: $ x_2 = 40 \cdot 4 = 160 \, \text{m} $. Total = $ 160 + 160 = 320 \, \text{m} $.

Question 2

A motorcycle accelerates uniformly from rest to $ 24 \, \text{m/s} $ in $ 6 \, \text{s} $. What is the distance traveled during this time?

Accepted Answer

Use $ x = v_0 t + \frac{1}{2} a t^2 $. First, find $ a = \frac{v - v_0}{t} = \frac{24 - 0}{6} = 4 \, \text{m/s}^2 $. Substitute: $ x = 0 \cdot 6 + \frac{1}{2} \cdot 4 \cdot (6)^2 = 0 + 2 \cdot 36 = 72 \, \text{m} $. The distance traveled is $ 72 \, \text{m} $.

Question 3

A car moving at $ 35 \, \text{m/s} $ decelerates uniformly to rest over $ 87.5 \, \text{m} $. What is the deceleration?

Accepted Answer

Use $ v^2 = v_0^2 + 2 a x $. Here, $ v = 0 $, $ v_0 = 35 \, \text{m/s} $, $ x = 87.5 \, \text{m} $. Substitute: $ 0 = (35)^2 + 2 a (87.5) \Rightarrow 0 = 1225 + 175 a \Rightarrow a = -7 \, \text{m/s}^2 $. Magnitude of deceleration is $ 7 \, \text{m/s}^2 $.

NEET Physics: Kinematics — Practice Set 11

Q1. A rocket accelerates from rest at \( 5 \, \text{m/s}^2 \) for \( 8 \, \text{s} \), then moves at constant speed for \( 4 \, \text{s} \). What is the total distance covered?

Q2. A motorcycle accelerates uniformly from rest to \( 24 \, \text{m/s} \) in \( 6 \, \text{s} \). What is the distance traveled during this time?

Q3. A car moving at \( 35 \, \text{m/s} \) decelerates uniformly to rest over \( 87.5 \, \text{m} \). What is the deceleration?

Q4. A car starts from rest and accelerates uniformly at \( 2 \, \text{m/s}^2 \) for \( 10 \, \text{s} \). What is the distance covered by the car during this time?

Q5. A particle moves at \( 20 \, \text{m/s} \) and decelerates at \( 4 \, \text{m/s}^2 \) until its speed is \( 8 \, \text{m/s} \), then accelerates at \( 3 \, \text{m/s}^2 \) to \( 20 \, \text{m/s} \). What is the total time taken?

Q6. A car accelerates uniformly from \( 10 \, \text{m/s} \) to \( 25 \, \text{m/s} \) over \( 150 \, \text{m} \), then decelerates to \( 5 \, \text{m/s} \) over the next \( 80 \, \text{m} \). What is the total time taken?

Q7. A train moving at \( 72 \, \text{km/h} \) decelerates at \( 1.5 \, \text{m/s}^2 \) for \( 8 \, \text{s} \), then at \( 3 \, \text{m/s}^2 \) until it stops. What is the total distance covered during deceleration?

Q8. A person walks \( 15 \, \text{m} \) in \( 5 \, \text{s} \) and then walks back \( 5 \, \text{m} \) in \( 1 \, \text{s} \). What is the average speed?

Q9. A car decelerates uniformly from \( 18 \, \text{m/s} \) to rest over a distance of \( 36 \, \text{m} \). What is the deceleration?

Q10. A ball is thrown upwards with a speed of \( 48 \, \text{m/s} \). How long does it take to return to the ground? (Take \( g = 10 \, \text{m/s}^2 \))