Handouts for Ch.2 Kinematics in 1-D
Distance is a scalar which measures length, whereas displacement is a vector which not only tells how far but also in which direction. Displacement is the shortest distance between the starting and ending point.
Speed tells how fast an object travels, and it is measured as distance over time
Speed = distance / time
Average speed is = total distance traveled / total time
Instantaneous speed gives speed at any instant of time, for example, the speedometer gives inst. speed.
Average Velocity = displacement / time ; and is a vector which points in the same direction as the displacement vector. If the total displacement in a trip is zero, then average velocity is zero. However, instantaneous velocity is not zero, if the object is moving during the trip.
Acceleration is the rate of change of velocity.
a = (final velocity – initial velocity) / time = (vf – vi) / t
When acceleration is constant, average velocity = (vf + vi) / 2
Acceleration vector does not necessarily point in the direction of the velocity vector.
All vectors, displacement, velocity & acceleration are negative if they point downward or due west, or due south. They are positive if they point upward or due East or due north.
An object is in free fall if its motion is affected only by gravity.
The acceleration due to gravity on the Earth’s surface is - 9.8 m/s2.
An object thrown up decreases its velocity by 9.8 m/s every second. The velocity becomes zero when it reaches maximum height.
Then the object changes direction and starts to fall downwards increasing its velocity by 9.8 m/s every second.
The total flight time in air is determined by the initial velocity of throw.
The time taken to go up is equal to the time to fall down.
At equal heights the magnitudes of velocities are equal and opposite in direction.
When solving problems in linear motion, follow the procedure
Identify clearly all the given variables and the unknown variables which you are asked to find. Put the correct units.
Identify the equation of kinematics which relates all the variables given and apply it
Put the correct sign + or – for all the variable vectors. If the object is falling down, then velocity and displacement are negative.
Assume that g = - 9.8 m/s2 if no planet is specified. If another planet is specified then do not assume the same. Remember once g is calculated for any planet it remains constant for all objects on that planet.
Air resistance is neglected and is zero.
If a number of questions are asked in a problem then do the solution in a stepwise manner, using the variables determined from previous steps, wherever applicable.
Look for hidden variables in problems, object dropped or starting from rest implies vi = 0. When it reaches maximum height vf = 0. g = a= - 9.8 m/s2.
The four equations of kinematics are valid if and only if acceleration is constant :
1.vf = vi + at
2.d = (vf + vi).t/2
3.d = vit + at2/2
4.vf2 – vi2 = 2.a.d
Graphical Analysis :
The distance vs time graphs for constant velocity give a straight line. The slope of the graph gives velocity. If the line is parallel to the x-axis, then velocity is zero
When velocity is changing and acceleration is constant, (for example a body in free fall), then the graph is a parabola. The slope of the tangent to the curve drawn at any given point gives the instantaneous velocity at that particular time.
Under constant acceleration the velocity vs time graph is a straight line, whose slope gives the acceleration. If the line is parallel to the x-axis then acceleration is zero.