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Q: A man walks on a straight road from his home to a market \$2.5\ km\$ away with a speed of \$5\ km\ h^{-1}\$ . Finding the market closed, he instantly turns and walks back home with a speed of \$7.5\ km\ h^{-1}\$. What is the (a) magnitude of average velocity, and(b) average speed of the man over the interval of time (i) \$0\$ to \$30\ min\$, (ii) \$0\$ to \$50\ min\$ (iii) \$0\$ to \$40\ min\$?

Distance to market \$s=2.5 km=2.5 \times 10^3=2500 m\$Speed with which he goes to market \$=5 km/h=5 \dfrac{10^3}{3600}=\dfrac{25}{18} m/s\$Speed with which he comes back \$=7.5 km/h=7.5 \times \dfrac{10^3}{3600}=\dfrac{75}{36} m/s\$(a)Average velocity is zero since his displacement is zero.(b) (i)Since the initial speed is 5km/s and the market is 2.5 km away,time taken to reach market:\$\dfrac{2.5}{5}=1/2 h=30\$ minutes.Average speed over this interval \$=5 km/h\$(ii)After 30 minutes,the man is travelling wuth 7.5 km/h speed for 50-30=20 minutes.The distance he covers in 20 minutes :\$7.5 \times \dfrac{1}{3}=2.5 km\$His average speed in 0 to 50 minutes: \$V_{avg}=\dfrac{distance \quad traveled}{time}\$\$=\dfrac{2.5+2.5}{(50/60)}=6 km/h\$(iii)In 40-30=10 minutes he travels a distance of :\$7.5 \times \dfrac{1}{6}=1.25 km\$\$V_{avg}=\dfrac{2.5+1.25}{(40/60)}=5.625 km/h\$

Q: Joseph Jogs from one end \$A\$ to the other end \$B\$ of a straight \$300\ m\$ road in \$2\$ minutes \$30\$ seconds and then turns around and jogs \$100\ m\$ back to point \$C\$ in another \$1\$ minute. What are Joseph's average speeds and velocities in jogging (a) from \$A\$ to \$B\$ and (b) from \$A\$ to \$C\$?

From pont A to BDistance covered\$=300m\$Displacement\$=300m\$Time taken\$=2\ min\ 30\ sec=(2\times60)+30=150\ sec\$Average speed\$=\frac{Distance\ covered}{Time taken}=\frac{300}{150}=2\ m/sec\$Average velocity\$=\frac{Displacement}{Time taken}=\frac{300}{150}=2\ m/sec\$From point A to CDistance covered\$=300+100=400m\$Displacement\$=300-100=200m\$Time taken\$=3\ min\ 30\ sec=(3\times60)+30=210\ sec\$Average speed\$=\frac{Distance\ covered}{Time taken}=\frac{400}{210}=1.90\ m/sec\$Average velocity\$=\frac{Displacement}{Time taken}=\frac{200}{210}=0.95\ m/sec\$

Q: A particle moving in a straight line covers half the distance with speed of \$3 \ m/s\$. The other half of the distance is covered in two equal time interval with speed of \$4.5\ m/s\$ and \$7.5\ m/s\$ respectively. The average speed of the particle during this motion is

\$\displaystyle t_{1}=\dfrac{\dfrac{S}{2}}{3}=\dfrac{S}{6}\$\$\displaystyle \dfrac{S}{2}=4.5\times t_{2}+7.5t_{3}\Rightarrow 12t_{2}=\dfrac{S}{2}\$We have \$t_2=t_3\$Total time \$\displaystyle t=t_{1}+t_{2}+t_3=\dfrac{S}{6}+\dfrac{S}{24}+\dfrac{S}{24}=\dfrac{S}{4}\$Average of \$\displaystyle \dfrac{S}{t}=\dfrac{S}{\dfrac{S}{4}}=4\: m/s\$

Q: The position of an object moving along x-axis is given by x = a + \$bt^2\$, where a = 8.5 m and b = 2.5 m \$s^{-2}\$ and t is measured in seconds. The average velocity of the object between t = 2 s and t = 4 s is

Position is given as \$x = a+bt^2 = 8.5+2.5t^2\$Position at \$t = 2 \ s\$, \$x_2 = 8.5+2.5(2)^2 = 18.5 \ m\$Position at \$t = 4 \ s\$, \$x_1 = 8.5+2.5(4)^2 = 48.5 \ m\$Displacement \$S = x_2-x_1 = 48.5-18.5 = 30 \ m\$Time taken \$t = 4-2 = 2 \ s\$Average velocity \$V_{avg} = \dfrac{S}{t} = \dfrac{30}{2} = 15 \ m/s\$

Q: A car travels from A to B at a, speed of \$20\, km\, h^{-1}\$ and returns at a speed of \$30\, km\, h^{-1}\$. The average speed of the car for the whole journey is:

Let distance from A to B be xTime for travel from A to B= x/20Time for travel from B to A= x/30Hence,speed for total distance 2x is: \$\dfrac{2x}{\dfrac{x}{30}+\dfrac{x}{20}}=\dfrac{2x\times60}{5x}\$=24 km\hr

Q: Abdul, while driving to school, computes the average speed for his trip to be \$20\$km \$h^{-1}\$. On his return trip along the same route, there is less traffic and the average speed is \$30\$km \$h^{-1}\$. What is the average speed for Abdul's trip?

Let us assume that Abdul is travelling \$x\$ kilometer distance while going to school.Distance = Speed x Time1)When it's average speed is 20 km/hr\${x}={v}_{1}\times{t}_{1}={20}\times{t}_{1}\$2)When it's average speed is 30 km/hr\${x}={v}_{2}\times{t}_{2}={30}\times{t}_{2}\$\${ V }_{ average }=\cfrac { total\quad distance\quad{travelled} }{ total\quad time\quad taken } \$\${ V }_{ average }=\cfrac { x+x }{ \frac { x }{ { v }_{ 1 } } +\frac { x }{ { v }_{ 2 } } } =\cfrac { 2x }{ \frac { x }{ 20 } +\frac { x }{ 30 } } =24\ {km\ h}^{-1}\$

Q: A car moving on a straight road covers one third of a certain distance with 20 Km/h and the rest with 60 Km/h. The average speed is :

Given,Velocity for one third of distance \$ {{V}_{1}}=20\,km/h \$ Velocity for two third of distance \$ {{V}_{2}}=60\,km/h \$ Time take to cover one third of distance \$ {{t}_{1}}=\dfrac{d/3}{{{V}_{1}}}=\dfrac{d/3}{20} \$ Time taken to cover two third of distance \$ {{t}_{2}}=\dfrac{2d/3}{{{V}_{2}}}=\dfrac{2d/3}{60} \$ \$ \text{Average velocity =}\dfrac{\text{Total}\,\text{distance}\,}{\text{total}\,\text{time}} \$ \${{V}_{av}}=\dfrac{d}{{{t}_{1}}+{{t}_{2}}}=\dfrac{d}{\dfrac{d/3}{20}+\dfrac{2d/3}{60}}=36\,km/h\$

Q: A car moves with a speed of 40 km/h for 15 minutes and then with a speed of 60 km/h for the next 15 minutes. The total distance covered by the car is :

Speed of car in first 15 minutes = 40 km/hDistance covered = speed \$\times \$ Time taken60 minutes = 1 hour15 minutes = \$\dfrac{15}{60}\$ hourDistance covered = \$240\times \dfrac{15}{60}=10 km\$Speed of car in next 15 minutes = 60 km/hDistance covered = \$60\times \dfrac{15}{60}=15 km\$\$\therefore \$ Total distance covered = (10+15)km = 25 km\$\therefore \$ 25 km is correct

Q: A motorcyclist drives from A to B with a uniform speed of \$30\ km\ h^{-1}\$ and returns with a speed of \$20\ km\ h^{-1}\$. Find the average speed.

Let the length of the line segment AB be \$x\ m\$The time taken is given as t=distance covered/speedTotal time = \${ t }_{ 1 }+{ t }_{ 2 } = \dfrac { x }{ 30 } +\dfrac { x }{ 20 } =\dfrac { 5x }{ 60 }\ h \$Average speed = Total distance/Total time = \$\dfrac { 2x }{ 5x/60 } =24\ km/h\$

Q: A car travels the first one third of a certain distance with a speed of 10 km/hr, the next one third with a speed of 20 km/hr and the last one third distance with a speed of 60 km/hr The average speed of the car for the whole journey is

Let the total distance travelled be x km Then total time taken = \$\displaystyle \frac{x/3}{10}+\frac{x/3}{20}+\frac{x/3}{60}=\frac{x}{30}+\frac{x}{60}+\frac{x}{180}\$\$\displaystyle =\frac{6x+3x+x}{180}=\frac{10x}{180}=\frac{x}{18}\$ hrs Then average speed = \$\displaystyle =\frac{Total\: distance\: travelled}{Total\: time\: taken}\$\$\displaystyle =\frac{x}{x/18}\$ km/hr = 18 km/hr

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Joseph Jogs from one end A to the other end B of a straight 300 m road in 2 minutes 30 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph's average speeds and velocities in jogging (a) from A to B and (b) from A to C?

A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time interval with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is

The position of an object moving along x-axis is given by x = a + bt2, where a = 8.5 m and b = 2.5 m s−2 and t is measured in seconds. The average velocity of the object between t = 2 s and t = 4 s is

A car travels from A to B at a, speed of 20kmh−1 and returns at a speed of 30kmh−1. The average speed of the car for the whole journey is:

Abdul, while driving to school, computes the average speed for his trip to be 20km h−1. On his return trip along the same route, there is less traffic and the average speed is 30km h−1. What is the average speed for Abdul's trip?

A car moving on a straight road covers one third of a certain distance with 20 Km/h and the rest with 60 Km/h. The average speed is :

A car moves with a speed of 40 km/h for 15 minutes and then with a speed of 60 km/h for the next 15 minutes. The total distance covered by the car is :

A motorcyclist drives from A to B with a uniform speed of 30 km h−1 and returns with a speed of 20 km h−1. Find the average speed.

A car travels the first one third of a certain distance with a speed of 10 km/hr, the next one third with a speed of 20 km/hr and the last one third distance with a speed of 60 km/hr The average speed of the car for the whole journey is

Joseph Jogs from one end $A$ to the other end $B$ of a straight $300 m$ road in $2$ minutes $30$ seconds and then turns around and jogs $100 m$ back to point $C$ in another $1$ minute. What are Joseph's average speeds and velocities in jogging (a) from $A$ to $B$ and (b) from $A$ to $C$ ?

A particle moving in a straight line covers half the distance with speed of $3 m / s$ . The other half of the distance is covered in two equal time interval with speed of $4.5 m / s$ and $7.5 m / s$ respectively. The average speed of the particle during this motion is

The position of an object moving along x-axis is given by x = a + $b t^{2}$ , where a = 8.5 m and b = 2.5 m $s^{- 2}$ and t is measured in seconds. The average velocity of the object between t = 2 s and t = 4 s is

A car travels from A to B at a, speed of $20 k m h^{- 1}$ and returns at a speed of $30 k m h^{- 1}$ . The average speed of the car for the whole journey is:

Abdul, while driving to school, computes the average speed for his trip to be $20$ km $h^{- 1}$ . On his return trip along the same route, there is less traffic and the average speed is $30$ km $h^{- 1}$ . What is the average speed for Abdul's trip?

A motorcyclist drives from A to B with a uniform speed of $30 k m h^{- 1}$ and returns with a speed of $20 k m h^{- 1}$ . Find the average speed.