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The rate of change of velocity of an object per unit time is called:
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Answer: Option C — Acceleration
Detailed Solution
Acceleration is the rate at which the velocity of an object changes with time. It is calculated as:
Acceleration (a) = Change in velocity / Time taken = (v – u) / t
where u is the initial velocity, v is the final velocity and t is the time taken. The SI unit of acceleration is metre per second squared (m/s²). Acceleration is a vector quantity: it has both magnitude and direction.
Since velocity includes both speed and direction, an object accelerates when its speed changes, when its direction changes, or both.
Types of acceleration:
- Positive acceleration: when velocity increases, such as a car speeding up after a traffic light turns green.
- Negative acceleration (retardation or deceleration): when velocity decreases, such as a car slowing down when brakes are applied.
- Uniform acceleration: when velocity changes by equal amounts in equal intervals of time, such as a freely falling object (ignoring air resistance).
- Non-uniform acceleration: when velocity changes by unequal amounts in equal intervals of time, such as a car moving in heavy traffic.
Centripetal acceleration: an object moving in a circle at constant speed, such as the Moon around the Earth, is always accelerating because its direction keeps changing. This acceleration is directed towards the centre of the circle.
The acceleration of an object falling freely under gravity near the Earth's surface is about 9.8 m/s². It is denoted by g.
For uniformly accelerated motion, the three equations of motion are:
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
- where s is the displacement.
On a velocity-time graph, the slope of the line gives the acceleration, and the area under the line gives the displacement. On a distance-time graph, a horizontal line shows that the object is at rest.
Why not the other options?
- ✗Speed is the distance travelled per unit time; it is a scalar.
- ✗Displacement is the shortest distance between the initial and final positions, in a given direction.
- ✗Momentum is the product of mass and velocity.
Quick tip
Remember: Acceleration = change in velocity / time (m/s²), a vector; uniform circular motion is accelerated; equations: v = u + at, s = ut + ½at², v² = u² + 2as; slope of v-t graph = acceleration.
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Motion, Force & Laws of Motion — Preparation
This question tests your understanding of Motion, Force & Laws of Motion, a key topic in the General Knowledge section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
This topic covers motion in a straight line and in a circle, speed, velocity and acceleration, Newton's three laws of motion, inertia, momentum and its conservation, friction, and centripetal and centrifugal forces. Exam questions often give an everyday example and ask which law explains it: passengers jerking forward when a bus stops suddenly shows inertia (the first law), and the recoil of a gun or the motion of a rocket shows the third law. Know the formulas for momentum (p = mv) and force (F = ma). Practise the motion and laws of motion questions below, written in the style of the general awareness sections of exams such as SSC, banking, railways, CUET GAT, MAH CET and CLAT. Each question comes with a detailed explanation that adds related facts, so every question helps you revise more than one point.