What is Acceleration?

 

Acceleration

Variable Velocity (or Non-uniform velocity)

 

The velocity of a body can be changed in any one of the following three ways :

(i) By changing the speed of the body,

(ii) By changing the direction of motion of the body, (iii) By changing both, the speed and direction of motion. Thus,

 

Velocity of a body is said to be variable (or non-uniform) when it covers unequal distances in a particular direction in equal intervals of time or the direction of motion of the body changes even when it covers equal distances in equal intervals of time.

 

 

It should be clearly understood that even when a body covers equal distances in equal intervals of time, but its direction of motion changes, the velocity of the body is said to be variable. Obviously, in such a situation, speed of the body is constant. For example, when a car rounds a curve at constant speed, it has a variable velocity, because its direction of motion changes continuously over the curve.

Average velocity

 

When a body is moving along a straight line at a variable speed, its velocity is variable. In that case, we express the rate of motion of the body in terms of its average velocity.

 

When velocity of a body is changing at a uniform rate over a period of time, then average velocity of the body for this period is arithmetic mean of initial velocity and final velocity of the body.

 

Average v=(u+v)/2

 

where u is the initial velocity, v is the final velocity and v_av is the average velocity of the body.

 

1.7. RATE OF CHANGE OF VELOCITY : CONCEPT OF ACCELERATION

 

When a body is moving uniformly along a straight line, its velocity is constant. Therefore, change in its velocity is zero, over any interval of time. However, when a body is in non-uniform motion, its velocity changes, i.e., velocity of the body is different at different points of the path and at different instants of time. Thus, the change in velocity of the body is not zero, during any interval of time. To express the rate of change of velocity, we introduce another physical quantity, called acceleration.

 

Acceleration of a body is defined as the rate of change of velocity of the body with acceleration of a body is a measure of change in velocity of the body per unit time.

 

 

a=(v-u)/t

 

i.e., unit of acceleration is metre per second square. It is written as m/s² or ms^-2. The other units of acceleration cm/s² and km/h². Note that unit of time occurs twice in the unit of acceleration.

 

If the motion is along a straight line and the velocity of the body is increasing with time, the acceleration is in the direction of velocity. Thus, acceleration is a vector quantity. The value of acceleration may be zero, positive or negative as discussed below :

(i) When a body is moving along a straight line with a uniform 0. Therefore, acceleration, a =v-u/t = U

 

(ii) When the velocity of a body increases with time, v > u. Therefore, (v - u) is positive and as such

a=v-u/t= positive

 

The direction of acceleration is along the direction of velocity. The motion is said to be accelerated motion. For example, when a body is dropped, its velocity goes on increasing (due to gravity). The acceleration is positive.

 

(iii) When the velocity of a body decreases with time, v< u. Therefore, (v – u) is negative and as such

a=v-u/t= negative

 

The negative acceleration is called retardation. The negative acceleration (or retardation) is in a direction opposite to the direction of velocity of the body. For example, when a body is thrown vertically upwards, its velocity goes on decreasing due to opposing gravity. The acceleration is negative. Similarly, when we apply brakes, the vehicle slows down due to negative acceleration or retardation.

 

Uniform Acceleration

 

The acceleration of a body is said to be uniform, when velocity of the body moving along a straight line changes by equal amounts in equal intervals of time, i.e., when velocity of a body changes at a uniform rate, it is said to have uniform acceleration.

 

For example :

 

(i) motion of a body falling freely under the action of gravity,

(ii) motion of a ball rolling down a smooth inclined plane,

 

(iii) motion of a bicycle going down the slope of a smooth road when there is no pedalling and air resistance is neglected.

 

Non-Uniform Acceleration

 

When the velocity of a body changes at a non-uniform rate, i.e., velocity changes by unequal amounts in equal intervals of time, the acceleration of the body is said to be variable or non-uniform.

 

On Your Tips

 

1. Speed of a body is a measure of rate of motion of the body. It is equal to distance travelled by the body in unit time

v=s/t

It is measured in m/s or cm/s or km/h.

 

2. Speed is a scalar quantity. It can be zero or positive. It can never be negative.

 

3. When a body travels equal distances in equal intervals of time, howsoever small the interval may be, the speed of the body is said to be uniform. When a body travels unequal distances in equal intervals of time, howsoever small the interval may be, the speed of the body is said to be non-uniform or variable. When speed is variable, we calculate average speed where total distance travelled a

 

1. Motion means movement.

2. The motion of an object is perceived when its position changes continuously with respect to some stationary object.

3. In certain situations, motion is inferred through indirect evidence.

4. The states of rest and motion are relative. An object may appear to be moving to one person, and the same object may appear to be at rest to another person.

5. To locate the position of an object, we have to choose some suitable reference point, called the origin.

6. The distance travelled by an object is the length of the actual path traversed by the object during motion.

7. The displacement of an object in motion is the shortest distance between the initial position and final position of the object.

8. Distance is a scalar quantity having magnitude only. Displacement is a vector quantity having both, the magnitude as well as direction.

9. The distance travelled by an object in motion can never be zero or negative. The displacement can be positive, zero or negative.

10. When final position of an object in motion coincides with its initial position, the displacement is zero, but the distance travelled is not zero.

11. Between two given positions, distance travelled can never be less than the displacement.

Thank You!!