Question

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{Question}}}}$
A particle moves 80 cm South in 0.12 seconds and then 60 cm West in 0.08 seconds. What is the magnitude of the average velocity of the particle?

A) 700 cm/s
B) 1417 cm/s
C) 500 cm/s
D) 250 cm/s
E) 709 cm/s

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Answer 1

Answer:

Explanation:

ANSWER:-

GIVEN:-

• For South :-
• Distance 80 cm
• Time = 0.12 seconds

• For West:-
• Distance = 60 cm
• Time = 0.08 seconds

Refer to Attachment for the Figure.

As it is forming a Right angle Triangle,

$\sf{(60)^2+(80)^2 = (x)^2}$ [Assuming x as third side)

$\sf{ 6400+3600 = x^2}$

$\sf{x^2 = 10000}\\\sf{x = 100 cm}$

Total Time taken will be

0.12+0.08 = 0.2 seconds.

Now we know the Formula that:-

$\sf{Velocity = \frac{Total \ Displacement}{Total \ time}}$

As we know that Hypotenuse will be the displacement, placing values we get the following:-

$\sf{ = \frac{100}{0.2}}$

$\boxed{\sf{ 500 \ cm/s \ is \ the \ answer}}$

Things to Note:-

• In this question answer were in cm/s so I did not convert it
• In general we need to convert it into m/s
• SI unit of Time is seconds
• Displacement is the shortest distance travelled.
• Hypotenuse will be considered as Displacement of the question.
• Pythagoras theorem was used in this Qustion which states that Sum of square of Base and height of a triangle will be equal to square of Hypotenuse of the triangle.

Answer 2

★ QUESTION :

A particle moves 80 cm South in 0.12 seconds and then 60 cm west in 0.08 seconds. What is the magnitude of the average velocity of the particle ?

GIVEN :

• A particle moves 80 cm (in south) for 0.12 seconds.

• That particle only moves 60 cm (in West) for 0.08 seconds.

TO FIND :

• Magnitude of average velocity of the particle = ?

STEP - BY - STEP EXPLAINATION :

Here, letters considered the third side of right angled triangle be 'x'

➠ (1st side)² + (2nd side)² = (3rd side)²

Substituting here the values as per the given formula

⟹ (60)² + (80)² = (x)²

⟹ (60×60) + (80×80) = x²

⟹ 3600 + 6400 = x²

➠ x = 100cm

➠ x² = 10,000

Time Taken to do it ----»

➠ 0.12 (from South)

➠ 0.08 (from west)

Now, here we will have to find the velocity, by applying here the formula of velocity -----›

⟹ Velocity = Total displacement / Total time taken

Substituting hear the values as per the given formula :

⟹ Velocity = 100/0.2 = 500 cm/s

Hence, magnitude of the average velocity of the particles is 500 cm/s.