Equations of Motion Questions

---

Very Short Answers Questions [1 Mark Questions]

Ques. Give the equation that shows the relationship between the initial velocity, final velocity, acceleration, and time.

Ans. The equation that shows the relationship between the initial velocity (u), final velocity (v), acceleration (a), and time (t) is

v = u + at

Ques. Give the equation that shows the relationship between displacement, initial velocity, time, and acceleration.

Ans. The equation that shows the relationship between displacement (S), initial velocity (u), time (t), and acceleration (a) is

S = ut + 1/2 at²

Ques. Give the equation that shows the relationship between final velocity, initial velocity, acceleration, and displacement.

Ans. The equation that shows the relationship between final velocity (v), initial velocity (u), acceleration (a), and displacement (S) is

v² = u² + 2aS

Ques. Give the equation that shows the relationship between displacement, final velocity, time, and acceleration.

Ans. The equation that shows the relationship between displacement (S), final velocity (v), time (t), and acceleration (a) is

S = vt - 1/2 at²

Ques. What are the variables that control the motion of an object with constant or uniform acceleration?

Ans. The quantities in the equation that control the motion of an object are displacement (S), acceleration (a), initial velocity (u), and final velocity (v).

---

Short Answers Questions [2 Marks Questions]

Ques. What is the equation of motion?

Ans. A mathematical formula that defines how a physical system acts over time is known as an equation of motion. The equation of motion defines the motion of objects and systems in terms of dynamic variables. These equations connect numerous key motion characteristics such as velocity, displacement, speed, time, and acceleration.

Ques. Define motion.

Ans. Motion is defined as a change in the position of an object over time with respect to a frame of reference. Displacement, distance, velocity, acceleration, time, and speed are all used to define motion.

Ques. What are the classic five equations of motion?

Ans. The following are the five equations of motion

• v = u + at
• S = ut + 1/2 at²
• v² = u² + 2aS
• S = vt - 1/2 at²
• S = 1/2 (u + v)t

Ques. What is meant by kinematics?

Ans. Kinematics is a branch of physics concerned with the study of the motion of an object without consideration for the cause of that motion.

Read More:

---

Long Answers Questions [3 Marks Questions]

Ques. What is the importance of equations of motion?

Ans. The following are the importance of equations of motion are

• The nature of the motion of the body is described using equations of motion. 
• The nature of a body is defined by the equation of motion as a set of mathematical functions involving dynamic variables. 
• Time and spatial coordinates are common examples of such variables. 
• It may include momentum components in some circumstances. 
• The most common options are generalized coordinates. 
• It can be any acceptable physical system-specific variable. 
• In classical mechanics, these functions are based on Euclidean geometry. 
• On the other hand, it is substituted by curved spaces in relativity.

Ques. What are the two descriptions of motion?

Ans. The two fundamental descriptions of motion are kinematics and dynamics.

• Kinematics: Kinematics is a straightforward approach to motion that simply considers variables obtained from the position and time of objects. These equations of motion are commonly referred to as the SUVAT equations in the case of constant acceleration. It was created using the following kinematic constraints: displacement 'S', initial velocity 'u', final velocity 'v', acceleration 'a', and time 't'.
• Dynamics: Dynamics, on the other hand, refers to complicated motion situations. Dynamic quantities such as energy and forces are considered. In this situation, the term dynamics refers to the differential equations that the object or system solves and, in some cases, the solutions of those equations.

Ques. Derive an equation for the distance traveled by a uniformly accelerated body in the nth second of its motion.

Ans. Let

• u be the initial velocity of the body
• a be the uniform acceleration of the body

The distance traveled by the body in the n second is given by

S_n = un + 1/2 an²

The distance traveled by the body in the (n-1) second is given by

S_n-1 = u(n - 1) + 1/2 a(n - 1)²

Distance traveled by the body in nth second is given by

S_n^th = S_n - S_n-1

⇒ S_n^th = [un + 1/2 an²] - [u(n - 1) + 1/2 a(n - 1)²]

On solving the above equation, we get

⇒ S_n^th = u + a/2 (2n - 1)

The above expression represents the equation for the distance traveled by a uniformly accelerated body in the nth second of its motion.

---

Very Long Answers Questions [5 Marks Questions]

Ques. A particle starts moving from a position of rest under constant acceleration. If it travels a distance x in t second, what distance will it travel in the next t second?

Ans. Given

• The initial velocity of the particle, u = 0
• The distance covered by the particle in time t second, S = x

Using the equation of motion S = ut + 1/2 at², we get

x = 0 + 1/2 at²

⇒ x = 1/2 at² …(i)

Let the particle travel y distance in the next t seconds.

The total distance traveled by the particle in (t + t = 2t) seconds will (x + y)

Again applying the equation of motion S = ut + 1/2 at², we get

x + y = 0 + 1/2 a (2t)²

⇒ x + y = 2at² …(ii)

Dividing equation (ii) by (i), we get

(x + y)/x = (2at² )/(1/2 at²)

⇒ (x + y)/x = 4

⇒ x + y = 4x

⇒ y = 3x

Hence the particle will cover a distance of 3x in the next t second.

Ques. A particle starts with an initial velocity of 2.0 m/s along the positive x-direction and it accelerates uniformly at the rate of 0.40 m/s²

1. Find the distance traveled by it in the first three seconds.
2. How much does it take to reach the velocity of 9.0 m/s?
3. How much distance will it cover in reaching the velocity of 9.0 m/s?

Ans. Given

• The initial velocity of the particle, u = 2 m/s
• The acceleration of the particle, a = 0.40 m/s²

1. For time, t = 3 s, using the equation of motion S = ut + 1/2 at², we get

Distance traveled, S = (2 x 3) + (1/2 x 0.40 x 3²)

⇒ S = 7.80 m

Hence the distance traveled by the particle in the first three seconds is 7.80 m.

2. Given the final velocity, v = 9 m/s

Using the equation of motion, v = u + at, we get

The time taken to reach velocity v is, t = (v - u)/a

⇒ t = (9 - 2)/0.40

⇒ t = 17.5 s

100. The time taken by the particle to reach the velocity v = 9 m/s is t = 17.5 s.

Therefore, the distance covered by the particle can be calculated by using the equation of motion S = ut + 1/2 at²

On substituting the values, we get

S = (2 x 17.5) + (1/2 x 0.40 x 17.5²)

⇒ S = 96.25 m

Ques. A particle having an initial velocity of 4 m/s moves with a constant acceleration of 1 m/s² for a time interval of 10 s in a straight line. Find the displacement of the particle in the last second and the total distance traveled in 10 s.

Ans. Given

• The initial velocity of the particle, u = 4 m/s
• Acceleration of the particle, a = 1 m/s²

The distance traveled by the particle in time t = 10 s is given by

S₁₀ = ut + 1/2 at²

⇒ S₁₀ = (4 x 10) + (1/2 x 1 x 10²)

⇒ S₁₀ = 90 m

The distance traveled by the particle in 10th second is given by

S₁₀^th = u + a/2 (2t - 1)

⇒ S₁₀^th = 4 + [1/2 (2 x 10 - 1)]

⇒ S₁₀^th = 13.5 m

Hence

• The total distance traveled in the last second (i.e. 10th second) is 13.5 m
• The displacement of the particle in 10 seconds is 90 m.

---

Previous Year Questions

1. Electric flux at a point in an electric field is..
2. The correct order of acid strength of the following carboxylic acids is..[Jee Advanced 2019]
3. The measurement of voltmeter in the following circuit is...[AIIMS 2017]
4. Angular velocity of minute hand of a clock is...[MP PMT 2004]
5. Highly pure dilute solution of sodium in liquid ammonia...[Jee Advanced 1998]
6. A gas mixture consists of 22 moles of oxygen and 44 moles of Argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is..[NEET UG 2017]
7. Alkali halides do not show Frenkel defect because​..
8. Let R = {(1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A = {1,2,3,4}. The relation R is...[AIEEE 2004]
9. Degree of freedom for polyatomic gas...[AIIMS 2012]
10. In pyrrole, the electron density is maximum on...[NEET UG 2016]
11. The major product of the following reaction is​...[JEE Main 2019]
12. Major product of the following reaction is..[JEE Main 2023]
13. The percentage of nitrogen in urea is about..
14. The electric field at a point is​
15. Which of the following statements is true?​..[JKCET 2006]

For Latest Updates on Upcoming Board Exams, Click Here: https://t.me/class_10_12_board_updates

---

Check-Out: