Average speed

Q. A boy runs for $10\text{min}$ at a uniform speed of $9\text{km/h}$. At what speed should be run for the next $20\text{min},$ so that the average speed comes to $12\text{km/h}$?

1. $10.5\text{km/h}$
2. $12.5\text{km/h}$
3. $13.5\text{km/h}$
4. $11.5\text{km/h}$

Q.

What will be the ratio between the magnitude of velocity and time?

Q.

A train travels $\frac{1445}{2}km$ in $\frac{17}{2}hours.$ Find the speed of the train in$\frac{km}{h}$.

Q. A car travels a distance of 300 km in 10 hours, the average speed of the car is

1. 15 km/hr
2. 10 km/hr
3. 30 km/hr
4. 20 km/hr

Q. A car travels first $\frac{1}{3^{\text{rd}}}$ of the distance $AB$ at $30\text{km/h}$, next $\frac{1}{3^{\text{rd}}}$ of the distance at $40\text{km/h}$, last $\frac{1}{3^{\text{rd}}}$ of the distance at $24\text{km/h}$. Its average speed for the whole journey is -

1. $40\text{km/h}$
2. $35\text{km/h}$
3. $30\text{km/h}$
4. $28\text{km/h}$

Q. A car travelled the first one-third of the distance $d$ at a speed of $5{\text{kmh}}^{-1}$, the second one-third of the distance at a speed of $10{\text{kmh}}^{-1}$ and the last one-third of the distance at a speed of $15{\text{kmh}}^{-1}$. Determine the average speed of the car(in $km/h$)

Q. A particle moves along the sides $AB,BC,$ and $CD$ of a square of side $25\text{m}$ shown in the figure. Time taken to reach point $D$ is $5\text{s}$. What is the average speed and magnitude of average velocity of the particle?

1. $25\text{m/s};5\text{m/s}$
2. $15\text{m/s};5\text{m/s}$
3. $25\text{m/s};15\text{m/s}$
4. $25\text{m/s};25\text{m/s}$

Q. A car moves through $20\text{km}$ with a speed of $40\text{km/hr}$ and the next $20\text{km}$ with a speed of $60\text{km/hr}$. Calculate its average speed.

1. $45\text{km/hr}$
2. $48\text{km/hr}$
3. $52\text{km/hr}$
4. $58\text{km/hr}$

Q. A man walks at a speed of $6\text{km/h}$ for $1\text{km}$ and $8\text{km/h}$ for next $1\text{km}$. What is his average speed for the walk of $2\text{km}$?

1. $5\text{km/h}$
2. $6\text{km/h}$
3. $7\text{km/h}$
4. $8\text{km/h}$

Q. A student starts from his physics classroom considered to be origin, walks $20m$ down the corridor, then stops, turns around and walks $5m$ back to his classroom. He stops $15m$ from the door. Total time of motion is $25.0sec$. What is his average speed?

1. $1m/s$
2. $2m/s$
3. $3m/s$
4. $4m/s$

Q. If the speed of a particle is given as $v=6t^2+2t\text{m/s}$, the speed of the particle at $2\text{sec}$ and the average speed in $4\text{sec}$ respectively is

1. $20\text{m/s},32\text{m/s}$
2. $28\text{m/s},36\text{m/s}$
3. $28\text{m/s},40\text{m/s}$
4. $24\text{m/s},36\text{m/s}$

Q. A car travel first $\frac{1}{3}rd$ of the total distance at $30\text{km/hr}$, next $\frac{1}{3}rd$ of the total distance at $40\text{km/hr}$ and last $\frac{1}{3}rd$ of the total distance at $24\text{km/hr}$. It's average speed in $\text{km/hr}$ for the whole Journey is

1. $40$
2. $35$
3. $30$
4. $28$

Q. If velocity of a particle is $v\left(t\right)=2t-4\text{m/s}$, the average speed and magnitude of average velocity of the particle in $5\text{sec}$ respectively are

1. $\frac{14}{5}\text{m/s},\frac{9}{5}\text{m/s}$
2. $\frac{13}{5}\text{m/s},\frac{9}{5}\text{m/s}$
3. $\frac{13}{5}\text{m/s},1\text{m/s}$
4. $\frac{14}{5}\text{m/s},1\text{m/s}$

Q. If the speed of a car is given as $v=2t+2\text{m/s}$, the average speed in $10sec$ is

1. $12\text{m/s}$
2. $10\text{m/s}$
3. $15\text{m/s}$
4. $20\text{m/s}$

Q. With what speed should a body be thrown upwards so that the distance traversed in $5^{th}$ second and $6^{th}$ second are equal? (Take $g=9.8m/s^2$)

1. $5.84\text{m/s}$
2. $49\text{m/s}$
3. $\sqrt{98}\text{m/s}$
4. $98\text{m/s}$

Q. Ramesh swims in a $90\text{m}$ long pool. He covers $180\text{m}$ in one minute by swimming from one end to the other and back along the same straight path. Find the average speed and average velocity of Ramesh, respectively.

1. $3{\text{ms}}^{-1},3{\text{ms}}^{-1}$
2. $3{\text{ms}}^{-1},0$
3. $0,3{\text{ms}}^{-1}$
4. $0,0$

Q.

If a car covers $2/5^{th}$ of the total distance with $v_1$ speed and $3/5^{th}$ distance with $v_2$ then average speed is

1. $\frac{1}{2}\sqrt{v_1{v}_2}$

2. $\frac{v_1+v_2}{2}$

3. $\frac{2v_1{v}_2}{v_1+v_2}$

4. $\frac{v_1{v}_2}{3v_1+2v_2}$

Q. If a car covers $2/5^{\text{th}}$ of the total distance with $v_1$ speed and $3/5^{\text{th}}$ distance with $v_2$, then the average speed is -

1. $\frac{1}{2}\sqrt{v_1{v}_2}$
2. $\frac{v_1+v_2}{2}$
3. $\frac{2v_1{v}_2}{v_1+v_2}$
4. $\frac{5v_1{v}_2}{3v_1+2v_2}$

Q. A truck travelled the first one-third of the distance $d$ at a speed of $10{\text{kmh}}^{-1}$, the second one-third of the distance at a speed of $12{\text{kmh}}^{-1}$ and the last one-third of the distance at a speed of $20{\text{kmh}}^{-1}$. The average speed of the truck is approximately equal to (in ${\text{kmh}}^{-1}$)

1. $10$
2. $13$
3. $15$
4. $17$

Q. If velocity of a particle is $v\left(t\right)=(15-3t)\text{m/s}$, the average speed of the particle in $6\text{sec}$ is

1. $5\text{m/s}$
2. $5.5\text{m/s}$
3. $6.5\text{m/s}$
4. $6\text{m/s}$

Q. If velocity $v$ of a particle as a function of position $x$ is given as $v=(\alpha -\beta x)$ where at $t=0,x=0$. Then,

1. Maximum displacement of particle is $\frac{\alpha }{\beta }$.
2. Maximum displacement of particle is $\infty$.
3. It takes $\infty$ time for particle to stop.
4. Time taken to reduce to half of initial velocity is $\frac{ln\left(2\right)}{\beta }$.

Q. A train travels from a city $A$ to city $B$ with a constant speed of $10\text{m/s}$ and returns back to city $A$ in half of the time taken to travel from $A$ to $B$. Find its average speed during the entire journey.

1. $40\text{m/s}$
2. $30\text{m/s}$
3. $15\text{m/s}$
4. $\frac{40}{3}\text{m/s}$

Q. If velocity of a particle is $v\left(t\right)=6t^2\text{m/s}$, the average speed of the particle in $6\text{sec}$ is

1. $60\text{m/s}$
2. $48\text{m/s}$
3. $72\text{m/s}$
4. $90\text{m/s}$

Q. If the speed of a car is given as $v=3t^2+2t\text{m/s}$, the average speed in $10sec$ is

1. $90\text{m/s}$
2. $110\text{m/s}$
3. $100\text{m/s}$
4. $120\text{m/s}$

Q. A car travels first half distance between two places with uniform speed of $60\text{km/hr}$. What should be its uniform speed (in $\text{km/hr}$) for the second half of the distance so that its average speed over the entire journey becomes $90\text{km/hr}$.

1. $120\text{km/h}$
2. $90\text{km/h}$
3. $60\text{km/h}$
4. $180\text{km/h}$

Q. A man walks on a straight road from his home to a market $2.5km$ away with a speed of $5km/h$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5km/h$. The average speed of the man over the interval of time $0$ to $40$ minutes, is equal to

1. $5km/h$
2. $\frac{25}{4}km/h$
3. $\frac{30}{4}km/h$
4. $\frac{45}{8}km/h$

Q. The position of the particle is given by $x=t^2+5t+2$ in $\text{m}$. The average speed of the particle in $6\text{sec}$ is

1. $11\text{m/s}$
2. $10\text{m/s}$
3. $13\text{m/s}$
4. $12\text{m/s}$

Q. If the speed of the particle is $v=4t^3+6\text{m/s}$, the distance of the particle as a function of time $t$ and the average speed in $3\text{sec}$ respectively are

1. $t^4-6t\text{m},33\text{m/s}$
2. $2t^4-6t\text{m},21\text{m/s}$
3. $t^4+6t\text{m},33\text{m/s}$
4. $t^3-6t\text{m},21\text{m/s}$

Q. A boy runs for $10\text{min}$ at a uniform speed of $9\text{km/h}$. At what speed should be run for the next $20\text{min},$ so that the average speed comes to $12\text{km/h}$?

1. $10.5\text{km/h}$
2. $12.5\text{km/h}$
3. $13.5\text{km/h}$
4. $11.5\text{km/h}$

Q. A car covers $40\text{km}$ at a uniform speed of $80\text{km/h}$ and the next $40\text{km}$ at a uniform speed of $100\text{km/h}$. Find the average speed of the car during its entire journey.

1. $82\text{km/h}$
2. $85\text{km/h}$
3. $89\text{km/h}$
4. $92\text{km/h}$