Motion in a Straight Line Flashcards
motion
if the position of an object is changing with time w.r.t. its surrounding, then the object is said to be in motion. Otherwise, it is at rest. So to describe the position of an object we need a reference or a set of coordinate axis(x, y and z axis).
Explain the meaning that motion and rest are relative.
Motion and rest are relative meaning that a body at rest w.r.t one person might be in motion w.r.t another person . This depends on the observer’s time refernce.
what is the frame of reference?
it is a set of coordinate axes attached to an observer having a clock with him to record time, w.r.t. which he can describe the motion of a moving object. If one or more coordinates of an object change with time, the object is said to be in motion. Otherwise, the object is said to be at rest w.r.t the time reference.
what is path length?
Distance or path length is the total actual path covered by the moving body. The distance can never be negative. Path length is a scaler quantity.
For a moving particle distance can never be 0. SI unit is m and Dimension is L
displacement
It is the shortest distance between the initial and final positions of the object in a partticular direction.
The magnitude of displcaement is always less than or equal to the total distance. It is a vector quantity.
For a moving object displacemnet can be 0. SI unit is m and Dimension is L. Displacement can have negative as well as postive values.
When is an object said to be in uniform motion in a straight line ?
An object is said to be in uniform motion in a straight line if its displacement is equal in equal intervals of time , however small the interval may be. Otherwise, the object is said to be in non-unifrom motion.
average velocity
change in position or displacemt of object divided by the time interval in which the displacement occurs
avg vel= change in postiton/ total time taken. x2-x1/t2-t1. When moving along a straight line, the path length or disatnce is equal to the magnitue of displacement. Thus avg vel is equal to avg speed which is defined as the total path length travelled divided by the total interval during which the motion has taken place.
avg speed= total distance travelled/total time interval.
if we dont move along a straight line, then the path length will have a greater magnitude than the displacement. In this case the avergae speed and velocity will be diff and the magnitude of avg speec will be greater than that of the avg velocity.
AVERAGE SPEED IS NOT THE MAGNITUDE OF AVG VELOCITY. displacemnt can be 0 then avg vel will be zero but avg speed is non zero.
some diffs between avg speed and avg velocity
avg speed is scaler
avg velocity is vector
both have same units and dimensions
Avg speed of a particle is never less than mag of avg vel as distance follows scaler addition and displacement follows vector addition.
an object may have varying avg vel without having varying avg speed as in case of unifrom circular motion as vel can chnage by even chnaging direction.
is vel is constant then speed will also be constant but if speed is constant then vel may or may not be constant as in case of unifrom circular motion.
significance of avg vel or avg speed
speed or vel of an object need not be constant. In most cases, objects will be in non uniform motion. so we describe the rate of motion of such objects in terms of their avg speed or vel.
why is position-time graph known as x-t graph
as we are dealing with objects mpving in straight line, so only x-coordinate is changing with time and therefore position time graph is also known as x-t graph.
slope to find v
v= x2-x1/t2-t1 or tan theta
instantaneous velocity
Gives the velocity of an object at a particular instant of time during a given interval.
so instantaneous vel of an object at a given instant of time is defined as the limit of avg vel as the time interval delta t becomes infinitely small.
if instantaneous vel remains constant throught an interval of time( like in uniform motion) then it is also equal to avg vel. But if instant vel is equal to avg vel then the motion may or may not be uniform.
Acceleration
defined as the rate of change of velocity with time. If velocity of an object changes by equal amount then accl is uniform but if the velocity is not changing by equal amount then there is variable accl and here we calculate average accl
Avg accl over a time interval is defined as the change of velocity divided by the time interval in which that change occurred.
vector a= v2-v1/t2-t1= delta v/delta t
SI unit = m/s^2
Accl can result from a change in speed(magnitude), or a change in direction or changes in both.
Accl can be positive, negative or 0
Instantaneous Acceleration
accl of the object at a particular instant of time during its motion and it is given as the time limit of the average acceleration of the object at a particular instant of time during its motion and it is given as the limit of the average acceleration at the time interval Delta t goes to 0
formula in aakash book
stopping distance
when brakes are applied to a moving vehicle, the disatnce it travels beofre stopping is called stopping disatnce. It is an important factor for road safety.
v^2-u^2=2as
s=u^2/2a
where s is stopping disatnce, u is initital vel, v is final vel and is 0 and a is retardation produced by brake.
Stopping distnace is proportional to the square of the initial velocity. Stopping disatnce is an important factor considered in setting speed limits.
