Average speed

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 body goes from A to B with a speed of $60\mathrm{Km}/\mathrm{h}$and then returns to the starting point with a speed of $40\mathrm{Km}/\mathrm{h}$.

Find (a) the average speed

(b) the average velocity of the body.

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.

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. $92\text{km/h}$

Q. The diagram shows the velocity against time graph for the motion of a body along a straight path. What is its displacement in the first $5\text{s}?$

1. $3\text{m}$
2. $5\text{m}$
3. $7\text{m}$
4. $9\text{m}$

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 travels from $A$ to $B$ at a speed of $20\text{km/h}$ and returns at a speed of $30\text{km/h}$. The average speed of the car for the whole journey is

1. $25\text{km/h}$
2. $24\text{km/h}$
3. $50\text{km/h}$
4. $5\text{km/h}$

Q.

To go home on Christmas Eve, Vinay travels by Bus at 80 km/hr (yes Bangalore bus service is awesome) from office to Bangalore Airport for $(\frac{1}{3}{)}^3$ of the total time. Then he travels by flight at 700 km/hr for next $(\frac{1}{3}{)}^3$ of time to reach Chennai Airport. Then he takes a cab to his house which travels at 120 km/hr (since its midnight). Find his average speed for the entire journey.

1. 700 km/hr

2. 100 km/hr

3. 300 km/hr

4. 80 km/hr

Q. Between the two stations, a train accelerates from rest uniformly at first, then moves with constant velocity and finally retards uniformly to come to rest. If the ratio of the time taken be $1:8:1$ and the maximum speed attained be $60\text{km/h}$, then, what is the average speed over the whole journey?

1. $48\text{km/hr}$
2. $52\text{km/hr}$
3. $54\text{km/hr}$
4. $56\text{km/hr}$

Q.

What is the average speed and average velocity till t = 20s?

1. 1 m/s, -1 m/s

2. 1m/s, 0

3. 0, 1 m/s

4. 0, 0

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. $120$
2. $150$
3. $180$
4. $210$

Q.

The figure shows four paths along which four different objects move from a starting point to a final point, all in the same time. The grid lines are equally spaced. Rank the paths according to the average speed, the greatest first.

1. $1,2,4,3$

2. $1,2,3,4$

3. $4,2,1,3$

4. $4,3,1,2$

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. 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 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 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 $0to40min$ 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 $x=t^2-6t$ in $\text{m}$. The average speed of the particle in $4\text{sec}$ is

1. $2.5\text{m/s}$
2. $3.5\text{m/s}$
3. $4.5\text{m/s}$
4. $3\text{m/s}$

Q. If a car covers $\frac{2}{5^{th}}$ of the total distance with $v_1$ speed and $\frac{3}{5^{th}}$ 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.

The figure shows four paths along which four different objects move from a starting point to a final point, all in the same time. The grid lines are equally spaced. Rank the paths according to the average speed, the greatest first.

1. $1,2,4,3$

2. $1,2,3,4$

3. $4,2,1,3$

4. $4,3,1,2$

Q.

What is the average speed and average velocity at t = 30s respectively?

1. 1 m/s, - 0.33 m/s

2. 1m/s, -1m/s

3. 2m/s, -0.25 m/s

4. 2 m/s, 0

Q. A particle is moving with speed $v=b\sqrt{x}$ along positive $x-$axis. Calculate the speed of the particle at time $t=\tau$ (assume that the particle is at origin at $t=0$)

1. $\frac{b^2\tau }{4}$
2. $\frac{b^2\tau }{2}$
3. $b^2\tau$
4. $\frac{b^2\tau }{\sqrt{2}}$

Q. Between two stations, a train accelerates uniformly at first, then moves with constant speed and finally retards uniformly. If the ratios of time taken are $2:1:2$ and the greatest speed is $10\text{km/hr}$, find the average speed over the whole journey.

1. $6\text{km/hr}$
2. $9\text{km/hr}$
3. $4.5\text{km/hr}$
4. $3\text{km/hr}$

Q. A particle starts from rest and travels a distance $l$ with uniform acceleration, then moves uniformly over a further distance $2l$ and finally comes to rest after moving a further distance $3l$ under uniform retardation. Assuming entire motion to be rectilinear motion the ratio of average speed over the journey to the maximum speed on its ways is

1. $1/5$
2. $2/5$
3. $3/5$
4. $4/5$

Q. A railway track runs parallel to a road until a turn brings the road to railway crossing. A cyclist rides along the road everyday at a constant speed $20\text{km/hr}$. He normally meets a train that travels in same direction at the crossing. One day he was late by 25 minutes and met the train $10\text{km}$ before the railway crossing. The speed of the train (in $\text{km/hr}$) is $30\text{N}$ , then $\text{N}$ is

Q.

Vijay has to go to office from home. He travels the first half of the distance at speed of 30 km/hr. For the remaining distance he travels at 10 km/hr for half the time and at 20 km/hr for the rest. Find his average speed.

1. 40 km/hr

2. 30 km/hr

3. 20 km/hr

4. 25 km/hr

Q. A particle moves along a straight line and its velocity depends on time as $v=6t-3t^2$ where $v$ is in $\text{m/s}$ and $t$ in seconds. Find the average speed for first 4 seconds. (in $\text{m/s}$)

Q. Figure shows a particle starting from point A, travelling upto B with a speed $s$, then upto point C with a speed $2s$ and finally upto A with a speed of $3s$. Find its average speed.

1. $1.2\text{s}$
2. $1.8\text{s}$
3. $2.4\text{s}$
4. $3\text{s}$

Q. If the speed of a particle is given as $v=6t^2+2t\text{m/s}$, the speed of the particle at $3\text{sec}$ and the average speed in $4\text{sec}$ respectively is

1. $60\text{m/s},36\text{m/s}$
2. $54\text{m/s},36\text{m/s}$
3. $60\text{m/s},32\text{m/s}$
4. $60\text{m/s},30\text{m/s}$

Q. A particle starts from rest and travels a distance $l$ with uniform acceleration, then moves uniformly over a further distance $2l$ and finally comes to rest after moving a further distance $3l$ under uniform retardation. Assuming entire motion to be rectilinear motion the ratio of average speed over the journey to the maximum speed on its ways is

1. $1/5$
2. $2/5$
3. $3/5$
4. $4/5$