Speed vs Velocity

Q. A particle of mass $m$ is at rest at the origin at time $t=0$. It is subjected to a force $F\left(t\right)=F_0{e}^{-bt}$ in the x-direction .Its speed $v\left(t\right)$ is depicted by which of the following curves ?

1. 
2. 
3. 
4. 

Q. A car is moving in a straight line with speed $18kmph$. It is stopped in $5s$ by applying the brakes. Find the speed of the car after $2s$ of applying the brakes.

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

Q. Which of the following quantities is a tensor?

1. Stress
2. Weight
3. Work
4. Temperature gradient

Q. A bus starting from rest moves with a uniform acceleration of $0.1m{s}^{-2}$ for $2minutes$. The distance travelled is:

1. $180m$
2. $720m$
3. $360m$
4. $900m$

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 speed of the particle (in $m/s$) is

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

Q. A bus moves from stop $A$ to the next stop $B$. Its acceleration varies as $a=\alpha -\beta x$, where $\alpha$ and $\beta$ are positive constants and $x$ is the distance from the stop $A$ to stop $B$. The distance between $A$ and $B$ and the maximum speed of the bus are

1. $\frac{2\alpha }{\beta }\text{and}\frac{\alpha }{\sqrt{\beta }}$
2. $\frac{\alpha }{\beta }\text{and}\frac{2\alpha }{\sqrt{\beta }}$
3. $\frac{\alpha }{\beta }\text{and}\frac{\alpha }{\sqrt{\beta }}$
4. $\frac{2\alpha }{\beta }\text{and}\frac{2\alpha }{\sqrt{\beta }}$

Q. A car travels half the distance with constant velocity 50 km/h and other half with a constant velocity of 40 km/h, along a straight line. The velocity if the car in km/h is:

1. 44.4
2. 45
3. 0
4. $\sqrt{(50\times 40)}$

Q. A car covers 30 km at a uniform speed of $60km{h}^{-1}$ and the next 30 km at a uniform speed of $40km{h}^{-1}$. Find the total time taken.

1. 45 min
2. 75 min
3. 30 min
4. 120 min

Q.

A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? Are the two equal?

Q.

Paragraph for below question
नीचे दिये गये प्रश्न के लिए अनुच्छेद

A particle is moving along x-axis such that its position as a function of time is x = 8t – 2t² (where x is in m and t is in s).
In reference to the above information, answer the following questions.

एक कण x-अक्ष के अनुदिश इस प्रकार गतिशील है कि समय के फलन के रूप में इसकी स्थिति x = 8t – 2t² (जहाँ x, m में है तथा t, s में है) है।

उपरोक्त सूचना के आधार पर निम्नलिखित प्रश्नों के उत्तर दीजिए।

Q. The particle reverses its direction of motion at time t equals to

प्रश्न - कण किस समय t पर अपनी गति की दिशा विपरीत करता है?

1. 2 s
2. 4 s
3. 3 s
4. 5 s

Q.

In the Left column, some of the physical quantities associated with a plane to plane projectile motion are mentioned. While in the Right column the description with time is given. Match the entries of the left column with the entries of the right column.

Column 1	Column 2
Horizontal component of velocity	Increasing
Speed of projectile	Constant
Acceleration of projectile	Decreasing
Horizontal and vertical displacement of projectile as measured from point of projections	Changing

Q. The velocity V of a body moving along a straight line varies with time $t$ as $v=2t^2{e}^{-t}$, where v is in m/s and $t$ in second . The acceleration of body is zero at $t$=

1. $0$
2. $2s$
3. $3$
4. Both (A) and (B)

Q. A body starts from origin and moves along x-axis such that at any instant velocity is $v_t=4t^3-2t$ where $t$ is in second and $v_t$ is in ${ms}^{-1}$. The acceleration of the particle when it is $2m$ from the origin is

1. $28{ms}^{-2}$
2. $22{ms}^{-2}$
3. $12{ms}^{-2}$
4. $10{ms}^{-2}$

Q. Which of the quantities, speed or velocity gives the direction of motion of body ?

1. speed
2. acceleration
3. velocity
4. all of the above

Q. Velocity is a vector quantity. State whether true or false.

1. True
2. False

Q. A particle moves according to the equation $\frac{dv}{dt}=\alpha -\beta v$ where $\alpha$ and $\beta$ are constants. Assuming particle starts from rest, it's velocity as a function of time will be

1. $v=\frac{\beta }{\alpha }(1-e^{-\beta t})$
2. $v=\frac{\beta }{\alpha }{e}^{-\beta t}$
3. $v=\frac{\alpha }{\beta }{e}^{-\beta t}$
4. $v=\frac{\alpha }{\beta }(1-e^{-\beta t})$

Q. Two boats A and B having same speed relative to river are moving ina river. Boat A moves normal to the river current as observed by an observer moving with velocity of river current.Boat B moves normal to the river as observed by the observer on the ground.

1. To a ground observer boat B moves faster than A.
2. To a ground observer boat A moves faster than B.
3. To the given moving observer boat B moves faster than A.
4. To the given moving observer boat A moves faster than B.

Q. Distinction between speed and velocity is :

1. speed is vector while velocity is scalar.
2. speed is scalar while velocity is vector.
3. speed and velocity are scalars.
4. speed and velocity are vectors.

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 speed of the particle (in $m/s$) is

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

Q.

Ram goes from point A to B by auto at the speed of 20 km/hr and comes back from B to A in a cab at a speed of 80 km/hr. Find his average speed.

1. 32 km/hr

2. 50 km/hr

3. 0 km/hr

4. 100 km/hr

Q.

Ram goes from point A to B by auto at the speed of 20 km/hr and comes back from B to A in a cab at a speed of 80 km/hr. Find his average speed.

1. 32 km/hr

2. 50 km/hr

3. 0 km/hr

4. 100 km/hr

Q. A particle of mass $m$ is at rest at the origin at time $t=0$. It is subjected to a force $F\left(t\right)=F_0{e}^{-bt}$ in the x-direction .Its speed $v\left(t\right)$ is depicted by which of the following curves ?

1. 
2. 
3. 
4. 

Q. A boy moving with a velocity of $20km/h$ along a straight line joining two stationary objects. According to him both objects

1. move in the same direction with the same speed of $20km/h$
2. move in different direction with the same speed of $20km/h$
3. move towards him
4. remains stationary

Q. A train accelerates from rest at constant rate of $\alpha$ for distance $X$ and time $T_1$ . After that it retards to rest at constant rate $\beta$ for distance $Y$ in time $T_2$ . Which of the following relations is correct?

1. $\frac{X}{Y}=\frac{a}{\beta }=\frac{T_1}{T_2}$
2. $\frac{X}{Y}=\frac{\beta }{\alpha }=\frac{T_1}{T_2}$
3. $\frac{X}{Y}=\frac{\alpha }{\beta }=\frac{T_2}{T_1}$
4. $\frac{X}{Y}=\frac{\beta }{\alpha }=\frac{T_2}{T_1}$

Q. If a velocity of a train which starts from rest is $72km/h\left(20m/s\right)$ after $5$ minutes, find out its acceleration and the distance traveled by the train in this time.

Q. Which graph(s) can represent the magnitude of the net force acting on the mass as a function of distance x?

1. I only
2. I and II only
3. II only
4. III only
5. II and III only

Q. Speed is a quantity but velocity is a quantity.

1. dimensionless
2. tensor
3. vector
4. scalar

Q. A particle moves with an initial velocity $v_0$ and retardation $\alpha v$, where $v$ is its initial velocity at any time $t$ and $\alpha$ is a constant

1. The particle will continue to move for a very long time.
2. The particle will come to rest after a time $\frac{1}{\alpha }$.
3. The particle will cover a total distance $\frac{v_0}{\alpha }$.
4. The velocity of the particle will become $\frac{v_0}{2}$ after a time $\frac{1}{\alpha }$.