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

Solving problems, questions, calculations, linear motion 1

1. A car moves in a straight line from a static state to a state of constant acceleration. After 1000 m, the car achieves a velocity of 240 m/s. Calculate

i) the acceleration of the car
ii) time taken
iii) the velocity at t= 2 s.

Answer:

From the question the information we can get is

a = 0 m/s
v = 240 m/s
s = 1000 m

i) For acceleration

We can use the formula v^2 = u^2 + 2as
Refer to (http://fiziknota.blogspot.com/2020/04/linear-motion-formula.html)

^2 is squared

When we rearrange the formula we get

a = (v^2 - u^2) / 2s

= 240^2 - 0^2 / (2 x 1000)

= 28.8 ms^-2

ii) for time

We have to rearrange v = u + at

t = (v - u)/ a

= (240) / 28.8

= 8.33 s

iii) velocity at t = 2 s. 

Using v = u + at

v = 0 + (28.8 x 2)

v = 57.6 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