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Acceleration is the rate at which the velocity of an object with respect to time changes.
- Since it has both a magnitude and a direction that makes it a vector quantity.
- The direction of the net force applied to an object determines the direction of its acceleration.
- The SI unit of acceleration is meters per second squared (ms-2).
According to Newton's Second Law, the amount of acceleration of an object is the combined result of two causes:
- The net resultant force i.e. vector sum of all external forces acting on that object.
- The mass of the object.
The formula of acceleration is given by
\(a = \frac{ \Delta v}{ \Delta t}= \frac{v_f-v_i}{t}\)
Where
- a is the acceleration produced in a body
- vf is the final velocity of the body
- vi is the initial velocity of the body
- Δt is the time taken to change the velocity from vi to vf
Very Short Answers Questions [1 Mark Questions]
Ques. What will be the acceleration of a body if it moves from rest and covers a distance of 6 m in 12 sec.?
- 0.22 ms-2
- 0.11 ms-2
- 0.08 ms-2
- 9.81 ms-2
Ans. The correct answer is c. 0.08 ms-2
Explanation: Using the equation of motion S = ut + 1/2 at2
We get
6 = 0 + 1/2(a x 122)
⇒ a = 12/144 = 0.08 ms-2
Ques. Negative acceleration is also known as
- Elevation
- Relaxation
- Escalation
- Deceleration
Ans. The correct answer is d. Deceleration
Explanation: Retardation, also known as deceleration, is the acceleration that occurs when motion is moving in the opposite direction.
Ques. The velocity of a truck fluctuates with time as v = 6t3. What is the acceleration at t = 3 s?
- 140 m/s2
- 160 m/s2
- 156 m/s2
- 162 m/s2
Ans. The correct answer is d. 162 m/s2
Explanation: Acceleration is given by
a = dv/dt
⇒ a = d/dt (6t3) = 18t2
For t = 3 s
a = 18 x 32 = 162 m/s2
Ques. Which among the following is an accurate depiction of the deceleration when a car is traveling in a north direction and produces a deceleration of 80 m/s2 to stop?
- Southwards, 80 m/s2
- Westwards, 80 m/s2
- Northwards, 80 m/s2
- Eastwards, 80 m/s2
Ans. The correct answer is a. Southwards, 80 m/s2
Explanation: The direction of motion of the car is along the North direction, but the car deaccelerates with a deceleration of 80 m/s2 to stop. The deceleration occurs in the opposite direction of the motion of the body, therefore the direction of deceleration of the car is along the South direction with a magnitude of 80 m/s2
Ques. What does the displacement-time graph of a uniformly accelerated motion look like?
- Parabola
- Hyperbola
- Ellipse
- Straight Line
Ans. The correct answer is a. Parabola
Explanation: In a uniformly accelerated motion, the acceleration is constant. From the equation of motion S = ut + 1/2 at2, the displacement-time graph represents a parabola.
Short Answers Questions [2 Marks Questions]
Ques. Define acceleration and state whether it’s a scalar or vector quantity.
Ans. Acceleration is the term used to describe how quickly a velocity varies over time, both in terms of speed and direction. An object is considered to be in accelerated motion when it accelerates or decelerates while traveling in a straight line. Due to the fact that it has both a magnitude and a direction, acceleration is a vector quantity.
Ques. What is uniform acceleration?
Ans. When an object moves in a straight line with an increase in velocity that occurs at equal intervals of time, then the body is said to be having uniform acceleration. An object falling freely is among the most common examples of uniform acceleration.
Ques. What is meant by the acceleration of free fall?
Ans. The acceleration caused by an object falling by the only gravitational pull of the Earth is known as the acceleration of free fall.
Ques. What is the acceleration due to gravity on Earth?
Ans. The acceleration produced by the gravitational pull of big masses is known as acceleration due to gravity (or acceleration of gravity) or gravity acceleration.
It is denoted by ‘g’. The value of acceleration due to gravity on the surface of the earth is 9.8 ms-2
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Long Answers Questions [3 Marks Questions]
Ques. What are the different types of acceleration?
Ans. The different types of acceleration are
- Uniform acceleration: An object is considered to be in uniform acceleration when it is moving in a straight line with a constant velocity increase occurring at regular intervals of time. The uniform acceleration of an object in free fall is an example of uniform acceleration.
- Non-uniform acceleration: Non-uniform acceleration is a situation in which an object experiences a uniform increase in velocity but not at exactly equal intervals of time. An example of non-uniform acceleration is a bus moving or leaving from the bus stop.
- Instantaneous acceleration: It is the acceleration of an object at any instance of time.
Ques. What are the different characteristics of acceleration?
Ans. The different characteristics of acceleration are
- It is a vector quantity because it has both magnitude and direction.
- The SI unit of acceleration is meters per second squared (ms-2)
- It can be positive, negative, or zero.
- When the velocity of the body increases over time, then positive acceleration occurs.
- When the velocity of the body decreases over time, then negative acceleration occurs.
- Negative acceleration is also known as retardation or deceleration.
- When the speed of an object remains constant then the acceleration of the object is zero.
- Acceleration can be related to the force using Newton’s second law of motion.
Ques. What are the applications of acceleration?
Ans. The followings are the applications of acceleration
- In the automobile sector, acceleration is essential since it determines how rapidly a vehicle can accelerate and how effectively it can brake. The design of spacecraft and aircraft must take acceleration into account.
- Acceleration is a key factor in determining an athlete's performance in sports like racing. Athletes need to accelerate as rapidly as they can to attain their peak speed.
- Acceleration is a tool that engineers use to create buildings that can experience forces like earthquakes and strong winds. When building tools and machinery which rotate or move at high speeds, they must also take acceleration into account.
Very Long Answers Questions [5 Marks Questions]
Ques. When two particles A and B are at point O, A is moving with a constant velocity of 50 m/s, while B is not moving. But possesses a constant acceleration of 10 m/s2. After how much time they will be at a distance of 125 m?
Ans. For particle A
- Initial velocity, uA = 50 m/s
- Acceleration, aA = 0
For particle B
- Initial velocity, uB = 0
- Acceleration, aB = 10 m/s2
The initial velocity of particle A with respect to particle B is given by
uAB = uA - uB = 50 - 0 = 50 m/s
Acceleration of particle A with respect to particle B is given by
aAB = aA - aB = 0 - 10 = – 10 m/s2
The distance between A and B after time t is given by
SAB = uABt + 1/2 aABt2
Given SAB = 125 m
⇒ 125 = 50t + 1/2 (-10)t2
⇒ t = 5 second
Ques. A bullet of mass 100 g fired from a gun moving with a velocity of 10 m/s hits a wooden log. The bullet stops after traveling a distance of 20 cm in the wooden log. Calculate the retarding acceleration of the bullet and the retarding force exerted by the log on the bullet.
Ans. Given
- The mass of the bullet, m = 100 g = 0.1 kg
- The initial velocity of the bullet, u = 10 m/s
- The distance covered by the bullet in the log, S = 20 cm = 0.2 m
Since the bullet finally stops, therefore its final velocity (v) is taken to be zero.
Using the equation of motion
v2 = u2 + 2aS
⇒ 0 = 102 + (2 x a x 0.2)
⇒ 0.4 a = 100
⇒ a = – 250 m/s2
The negative sign shows the retardation of the bullet.
Now retarding force can be calculated by using Newton’s second law of motion
F = ma
⇒ F = 0.1 x (-250) = – 25 N
Ques. A body of mass 50 kg stands on a weighing machine lying on the floor of a lift. What will be the weight of the body when
- The lift moves upward with acceleration, a = 2.2 m/s2
- The lift moves downward with acceleration, a = 2.2 m/s2
- The falls freely
Ans. Given
- The mass of the body, m = 50 kg
- Acceleration of the lift, a = 2.2 m/s2
- Acceleration due to gravity, g = 9.8 m/s2
The weight of the body in a weighing machine is the normal reaction exerted by the weighing machine on the body.
- When the lift moves upward, the normal reaction is given by
N = m(g + a) = 50(9.8 + 2.2) = 50 x 12 = 600 N
- When the lift moves downward, the normal reaction is given by
N = m(g - a) = 50(9.8 - 2.2) = 50 x 7.6 = 380 N
- When the lift falls freely, then a = g, therefore the normal reaction is given by
N = m(g - g) = 0
The body will be in a state of weightlessness.
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