#### IIT (NTSE/Olympiad)

# Motion in one Dimension

__Points to Remember - Motion in One Dimension__

__Points to Remember - Motion in One Dimension__

**1.**If body starts from rest or falls freely or is dropped then, u = 0.

**2.**If the body is thrown upwards then it will rise until its vertical velocity becomes zero. Maximum height attained is h = u

^{2}/2g.

**3.**If air resistance is negligible then the time of the rise is equal to time of fall and each is equal to t = u/g.

**4.**The body returns to the starting point with the same speed with which it was thrown.

**5.**The straight line inclined to time axis in x-t graph represents constant velocity.

**6.**In x-t graph the straight line inclined to time axis at an angle greater than 90º shows negative velocity.

**7.**No line in x – t graph can be perpendicular to time axis because it will represent infinite velocity.

**8.**If the x – t graph is a curve whose slope decreases continuously with time, then the velocity of the body goes on decreasing continuously and the motion of the body is retarded.

**9.**If the v – t graph is a straight line parallel to time axis, then the acceleration of the body is zero.

**10.**If the graph is a straight line inclined to time axis with positive slope, then that body is moving with constant acceleration.

**11.**If v – t graph is a straight line inclined to time axis with negative slope, then the body is retarded.

**12.**Velocity and acceleration of a body need not be zero simultaneously.

**13.**A body in equilibrium has zero acceleration only. All other quantities need not be zero.

**14.**If a body travels with a uniform acceleration a

_{1}for a time interval t1and with uniform acceleration a

_{2}for a time interval t

_{2}, then the average acceleration a =

**15.**For a body moving with uniform acceleration, the average velocity (u + v)/2, where u is the initial velocity and v is the final velocity.

**16.**The distance travelled by the body in successive second in the ratio 1 : 3 : 5 : 7 .......etc.

**17.**When the body is starting from rest, the distances travelled by the body in the first second, first two seconds, first three seconds, etc. are in the ratio of 1 : 4 : 9 : 16 : 25 ........etc.

**18.**When a body is dropped freely from the top of the tower and another body is projected horizontally from the same point, both will reach the ground at the same time.

**19.**If the v – t graph is a curve whose slope decreases with time then the acceleration goes on decreasing.

**20.**If the v-t graph is a curve whose slope increases with time then the acceleration of the body goes on increasing.

**21.**The v-t graph normal to time axis is not a practical possibility because it means that the acceleration of the body is infinite.

**Various Graphs Related to Motion :****A. Displacement-Time Graph** : ** (a)** For a stationary body **(b)** For a body moving with constant velocity**(c)** For a body moving with non-uniform velocity**(d)** For a body with accelerated motion ** (e)** For a body with decelerated motion**(f) **For a body which returns towards the point of reference** (g)** For a body whose velocity constantly changes**(h)** For a body whose velocity changes after certain interval of time**B. Velocity-Time Graph:**** (a)** For the body having constant velocity or zero acceleration ** (b)** When the body is moving with constant retardation and its initial velocity is not zero** (c)** When body moves with non-uniform acceleration and its initial velocity is zero.

**C. Acceleration-Time Graph :** ** (a)** When acceleration is constant

**(b)** When initial acceleration is zero and rate of change of acceleration is non-uniform

#### IIT (Class X)

- Unit, Dimension & Error

- Vectors

- Motion in One Dimension
- Distance
- Displacement
- Comperative Study of Distance & Displacement
- Speed
- Velocity
- Comparative Study of Instantaneous Speed and Instantaneous Velocity
- Comparative Study Of Average Speed & Average Velocity
- Acceleration
- Motion With Uniform Acceleration
- Motion Under Gravity
- Relative – Velocity
- Points to Remember - Motion in One Dimension

- PROJECTILE MOTION

- NEWTON'S LAWS OF MOTION & FRICTION

- WORK, POWER, ENERGY & CONSERVATION LAWS

- CIRCULAR MOTION & ROTATIONAL DYNAMICS

- GRAVITATION