Finding Average Velocity

Q.

A car travels along a straight line for first half time with speed $40km/hr$ and the second half time with speed $60km/hr$. Find the average speed of car.

Q.

On a 60km track, a train travels the first 30km with a speed of $30km/h$. How fast must the train travel the next 30km so as to average $40km/h$ for the whole trip?

Q.

A car covers 20 km in 2 hours. Calculate the speed of the car?

Q.

An object moves the first half of the total distance with a speed of $2m{s}^{-1}$. If the average speed of the body is $3m{s}^{-1}$, the speed of the body when it traveled the remaining distance is ___________ $m{s}^{-1}$.

1. 3

2. 6

3. 4

4. $2$

Q. A body covers one-third of the distance with a velocity $v_1$, the second one-third of the distance with a velocity $v_2$ and the remaining distance with a velocity $v_3$. The average velocity is

1. $\frac{v_1+v_2+v_3}{3}$
2. $\frac{3v_1{v}_2{v}_3}{v_1{v}_2+v_2{v}_3+v_3{v}_1}$
3. $\frac{v_1{v}_2+v_2{v}_3+v_3{v}_1}{3}$
4. $\frac{v_1{v}_2{v}_3}{3}$

Q.

A car covers a distance of 500 km with an average speed of 10 km h-¹. How much time does it take to cover the distance?

Q.

A car is travelling $48km$ in one hour. The distance travelled by the car in $12mins$ is _________.

Q. A body covers first one-third of its journey with speed $u$, next one- third with speed $v$ and the last one-third with speed $w$. Calculate the average speed of the body over the entire journey.

1. $\frac{uvw}{uv+vw+uw}$
2. $\frac{3uvw}{uv+vw+uw}$
3. $\frac{2uvw}{uv+vw+uw}$
4. $\frac{4uvw}{uv+vw+uw}$

Q. Statement - 1 : For a particle undergoing rectilinear motion with constant acceleration, the average velocity cannot be equal for two different time intervals.
Statement -2 : The average velocity of particle moving with constant acceleration in a time interval is $\frac{\overrightarrow{u}+\overrightarrow{v}}{2}$ ,
where $\overrightarrow{u}$ is the initial velocity and $\overrightarrow{v}$ is the final velocity.

1. Both statement 1 and statement 2 are correct and statement 2 is the correct explanation of statement 1.
2. Both statement 1 and statement 2 are correct but statement 2 is not the correct explanation of statement 1.
3. Statement 1 is correct and statement 2 is incorrect.
4. Statement 1 is incorrect and statement 2 is correct.

Q. A car’s odometer reads $22687\text{km}$ at the start of a trip and $22791\text{km}$ at the end of the trip. If the trip takes 4 hours, then the average speed of the car in (i) ${\text{km h}}^{-1}$ (ii) ${\text{m s}}^{-1}$ is

1. (i) 20 (ii)5.55
2. (i) 36 (ii) 10
3. (i) 18 (ii) 5
4. (i) 26 (ii) 7.2

Q. Find the average velocity of the position function $s\left(t\right)=2t^2-4t$ on the interval from $t=0\text{sec}$ to $t=5\text{sec}$.

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

Q. A particle moves along a semicircle of radius $10\text{m}$ in 5 seconds. The magnitude of average velocity of the particle is

1. $2\pi m{s}^{-1}$
2. $4\pi m{s}^{-1}$
3. $2m{s}^{-1}$
4. $4m{s}^{-1}$

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. A car runs at a constant speed on a circular track of radius $200\text{m}$, taking $62.8\text{s}$ on each lap. Find the average velocity(in $\text{m/s}$) and average speed(in $\text{m/s}$) respectively in each lap.

1. $20$ and zero
2. $0$ and $20$
3. $20$ and $20$
4. $6.3$ and $20$

Q. If a particle has velocity $v\left(t\right)=18-6t\text{m/s}$, the magnitude of average velocity in $10\text{sec}$ is

1. $-10\text{m/s}$
2. $12\text{m/s}$
3. $10\text{m/s}$
4. $-8\text{m/s}$

Q. A particle is moving in a circle of radius $R$ with constant speed. The time period of the particle is $T$. In a time $t=\frac{T}{6}$, the magnitude of average velocity of the particle is

1. $\frac{3R}{T}$
2. $\frac{6R}{T}$
3. $\frac{2R}{T}$
4. $\frac{4R}{T}$

Q. Length of the minute hand in a clock is $10\text{cm}$. Find difference between average speed and magnitude of average velocity (in $cm/min$) of tip of the minute hand from $6$ a.m. to $6:20$ a.m.

1. $\frac{2\pi }{3}-\frac{\sqrt{3}}{2}$
2. $\frac{2\pi }{3}-\frac{1}{2}$
3. $\frac{\pi }{3}-\frac{\sqrt{3}}{2}$
4. $\frac{\pi }{3}-\frac{1}{2}$

Q. A particle moves along a semicircle of radius $10\text{m}$ in 5 seconds. The magnitude of average velocity of the particle is

1. $2\pi m{s}^{-1}$
2. $4\pi m{s}^{-1}$
3. $2m{s}^{-1}$
4. $4m{s}^{-1}$

Q.

A student walks to his school at a distance of 8 km with a constant speed of 2 km/h and walks back at a constant of 4 km/h. Calculate the average speed of the round trip.

Q. If velocity of a particle is $v\left(t\right)=6-2t\text{m/s}$, the average speed and magnitude of average velocity of the particle in $5\text{sec}$ respectively are

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

Q. The position of the particle is given by $x=3t^3+4$ in $\text{m}$. The average speed of the particle in $3\text{sec}$ is

1. $22\text{m/s}$
2. $25\text{m/s}$
3. $27\text{m/s}$
4. $29\text{m/s}$

Q. A particle starts from $x=0$ and moves along a straight line such that its velocity $v$ depends on position $x$ as $v=x+4$. For the first four seconds, average velocity of the particle (in $m/s$) is

1. $e^4+1$
2. $e^4-1$
3. $e^4+4$
4. $e^4-4$

Q. If a particle has velocity $v\left(t\right)=t^2-7t+12$, the average speed in $6\text{sec}$ is

1. $\frac{50}{6}\text{m/s}$
2. $\frac{55}{18}\text{m/s}$
3. $\frac{61}{18}\text{m/s}$
4. $\frac{43}{6}\text{m/s}$

Q. Statement 1: Magnitude of average velocity is equal to average speed, if velocity is constant.
Statement 2: If velocity is constant, then there is no change in the direction of motion.

1. Statement-1 is True; Statement-2 is True; Statement -2 is a correct explanation for Statement-1.
2. Statement-1 is True; Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1.
3. Statement-1 is True; Statement-2 is False.
4. Statement-1 is False; Statement-2 is True

Q. A truck driver drives $20\text{km}$ down the road in $5\text{minutes}$ . He then reverses and drive $12\text{km}$ back down the road in $3\text{minutes}$. What is the average velocity?

1. $1\text{km/min}$
2. $2\text{km/min}$
3. $3\text{km/min}$
4. $4\text{km/min}$

Q. If velocity of a particle is $v\left(t\right)=6-2t\text{m/s}$, the average speed and magnitude of average velocity of the particle in $5\text{sec}$ respectively are

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

Q. If velocity of a particle is $v\left(t\right)=(9-3t)\text{m/s}$, the average speed and magnitude of average velocity of the particle in $4\text{sec}$ respectively are

1. $5.5\text{m/s},5\text{m/s}$
2. $3.75\text{m/s},3\text{m/s}$
3. $3.5\text{m/s},3\text{m/s}$
4. $5.75\text{m/s},5\text{m/s}$

Q. A particle moves according to the equation $x=t^2+3t+4$ . The average velocity in the first $5\text{s}$ is

1. $8{\text{ms}}^{-1}$
2. $7.6{\text{ms}}^{-1}$
3. $6.4{\text{ms}}^{-1}$
4. $5.8{\text{ms}}^{-1}$

Q. If velocity of a particle is $v\left(t\right)=(3t^2-2t+4)\text{m/s}$, the magnitude of average velocity of the particle in $10\text{sec}$ is

1. $94\text{m/s}$
2. $88\text{m/s}$
3. $104\text{m/s}$
4. $90\text{m/s}$

Q. A body traveling along a straight line traversed first one third of the total distance with a velocity $3\text{m/s}$. The remaining part of the distance was covered with a velocity $2\text{m/s}$ for half the time and with velocity $6\text{m/s}$ for the other half of time. The mean velocity over the whole time of motion is

1. $5\text{m/s}$
2. $4\text{m/s}$
3. $4.6\text{m/s}$
4. $3.6\text{m/s}$