Solving problems, questions, calculations, linear motion 2

Look at the diagram above. It is a displacement-time graph for a moving object.

Questions:

a) What is the displacement of the object at t = 2 s?

Answer = 20 m

b) When does the object cease to move?

Answer = From t = 4 s until t = 8 s

c) When does the object starts to move in the opposite direction?

Answer = At t = 8 s.

d) What is the velocity of the object at time

i) t = 6 s?

Answer = the object is not moving at all, hence velocity is zero.

ii) t = 9 s?

Gradient of the graph, as t = 9 is in the middle of the movement.

Hence v = - 40 / 2 = - 20 m/s

* Note the negative sign which indicates that the object is moving in the opposite direction.

e) Calculate the total distance traveled?

40m + 80m = 120 m, note that the direction of the movement does not matter here as distance is a scalar quantity.

f) Calculate the total displacement traveled?

+40m = ( - 80m) = -40m

Note that the total displacement is negative indicating the final position is -40m opposite the first direction of travel.

g) What is the average speed of the object?

Average speed =  distance / time
= 120 / 12 = 10 m/s

h) What is the average velocity of the object

Average velocity  = total displacement / time

= -40 / 12
= 3.33 m/s

Linear Motion Formula

Below are the common formula for Linear Motion:



Where

v = final velocity
u = initial velocity
s = displacement
a = acceleration
t = time

Analysing linear motion

General Definition:

Distance: length between two points in a straight line or length moved through a definite path.

Displacement: Distance moved in a definite direction (vector quantity).

Speed: distance moved per unit time.

Velocity: rate of change in displacement.

Average speed: (total distance/total time)

Average velocity (total displacement/ total time)

Constant velocity: rate of change in displacement is constant (zero acceleration).

Positive acceleration means that the velocity is increasing.

Negative velocity means that the acceleration is negative and the velocity decreases.

Period, T, is the time taken for a complete oscillation. Unit: s-1

Frequency,f, is the number of oscillations made in one second. Unit: Hz

A ticker timer is used to measure a short period of time in linear motion. One dot is the period of time taken between two consecutive dots on a ticker tape. If the frequency used is 50 Hz, the period for one dot is then 0.02 s.

A stroboscope is used to 'freeze' the motion of an oscillation to determine its frequency, where frequency of the oscillation equals frequency of stroboscope.

Frequency of stroboscope = number of slits X frequency of rotation.