Question

The velocity-time (v-t) graph of a particle moving along a straight line is shown below. Find the average velocity

of the particle in km/h.​

Answer 1

Given : velocity-time graph.

To Find : Draw the distance-time graph

average velocity

Solution:

at t = 0   , S = 0  

S = (1/2)(u + v) * t  ,  v = u + at  

at t = 1   v = 2  =>   S =  (1/2)(0  + 2) * 1   = 1

at t =2  v = 4  => S = (1/2)(0 + 4) * 2  =   2

at t =3 v = 6  => S = (1/2)(0 + 6) * 3  =   9

at t =4  v = 8  => S = (1/2)(0 + 8) * 4 =   16

at t =5  v = 10  => S = (1/2)(0 + 10) * 5 =   25

from t = 5 to t = 10  v  is constant 10

Hence at

t = 6   S = 25 + 10* 1  = 35

t = 7   S = 25 + 10* 2 =  45

t = 8   S = 25 + 10* 3  = 55

t = 9  S =  25 + 10* 4 =  65

t =10   S = 25 + 10* 5  = 75

from t = 10 to 15

t = 11  ,  S =  75  +  (1/2)(10 + 8) * 1  =   84

t = 12  ,  S =  75  +  (1/2)(10 + 6) * 2 =  91

t = 13  ,  S =  75  +  (1/2)(10 + 4) *3 =   96

t = 14  ,  S =  75  +  (1/2)(10 + 2) *4 =   99

t = 15  ,  S =  75  +  (1/2)(10 + 0) *5 =  100

Now plot points :

distance-time graph is plotted

Total Distance =  100   m

Time = 15 sec

Average velocity =  100/15  =  20/3  = 6.67 m/s

in km/hr  = (20 / 3) * (3600 / 1000) = 24 km/hr

Learn More:

A car starts from rest and travels for 30 minutes at 50 km per hour it ...

brainly.in/question/13820843

A towns A and B are 80km apart.A cyclist starts from A at 8 am and ...

brainly.in/question/15166749

Answer 2

Given:

The velocity-time (v-t) graph of a particle moving along a straight line is shown below.

To find:

Average Velocity?

Calculation:

Average Velocity can be calculated from the ratio of total displacement and total time.

$\rm \: avg. \: v = \dfrac{total \: displacement}{total \: time}$

• Now 'total displacement' can be calculated from the area under velocity-time graph.

$\rm \implies\: avg. \: v = \dfrac{area \: of \: trapezium}{total \: time}$

$\rm \implies\: avg. \: v = \dfrac{ \dfrac{1}{2}(sum \: of \: || sides) \times (\perp \: d) }{total \: time}$

$\rm \implies\: avg. \: v = \dfrac{ \dfrac{1}{2}(5 + 15) \times (10) }{15}$

$\rm \implies\: avg. \: v = \dfrac{ \dfrac{1}{2} \times (20) \times (10) }{15}$

$\rm \implies\: avg. \: v = \dfrac{ 100 }{15}$

$\rm \implies\: avg. \: v = 6.66 \: m {s}^{ - 1}$

$\rm \implies\: avg. \: v = 6.66 \times \dfrac{18}{5}\: km/hr$

$\rm \implies\: avg. \: v = 24\: km/hr$

So, average velocity is 24 km/hr