Question

8.
When a body covers first one third distance with speed 1m/s, the second one third distance
with speed 2m/s and the last one third distance with speed 3m/s then average speed is
1) 2.24 m/s
2) 1.79 m/s
3) 2.66 m/s
4) 1.64 m/s​

Answer 1

Answer:

option 2

Explanation:

avg speed = total dis/total time

so total distance = X

t1 = (1/3x)/1

t2=(1/3x)/2

t3=(1/3x)/3

avg speed =  avg speed = (t1+t2+t3)/x

=11/6m/s=1.8m/s

Answer 2

Answer:

The average speed of the body is 1.64m/s i.e.option(4).

Explanation:

The average speed is calculated as,

$\mathrm{V_{avg}=\frac{d}{T} }$        (1)

Where,

$\mathrm{V_{avg} }$=average speed

T=total time

From the question, we have the following cases,

First one-third distance

Distance traveled(x₁)=$\mathrm{\frac{d}{3} }$

The speed with which the body travels(v₁)=1m/s

Calculating the amount of time needed to travel this distance,

$\mathrm{t_1=\frac{x_1}{v_1} }$         (2)

Inserting the values in equation (2) we get;

$\mathrm{t_1=\frac{\frac{d}{3} }{1} }$

$\mathrm{t_1=\frac{d}{3} }$           (3)

Second one-third distance

Distance traveled(x₂)=$\mathrm{\frac{d}{3} }$

The speed with which the body travels(v₂)=2m/s

Calculating the amount of time needed to travel this distance,

$\mathrm{t_2=\frac{x_2}{v_2} }$           (4)

Inserting the values in equation (4) we get;

$\mathrm{t_2=\frac{\frac{d}{3} }{2} }$

$\mathrm{t_2=\frac{d}{6} }$      (5)

Third one-third distance

Distance traveled(x₃)=$\mathrm{\frac{d}{3} }$

The speed with which the body travels(v₃)=3m/s

Calculating the amount of time needed to travel this distance,

$\mathrm{t_3=\frac{x_3}{v_3} }$                (6)

Inserting the values in equation (6) we get;

$\mathrm{t_3=\frac{\frac{d}{3} }{3} }$

$\mathrm{t_3=\frac{d}{9} }$         (7)

Now by placing values in equation (1) we get;

$\mathrm{V_{avg}=\frac{d}{t_1+t_2+t_3} }$

$\mathrm{V_{avg}=\frac{d}{\frac{d}{3} +\frac{d}{6} +\frac{d}{9} } }$

$\mathrm{V_{avg}=\frac{d}{\frac{11d}{18} } }$

$\mathrm{V_{avg}=\frac{18}{11}\ m/s }$

$\mathrm{V_{avg}\approx 1.64 \ m/s }$

Hence, the average speed of the body is 1.64m/s i.e.option(4).

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