Magnitude and Direction of Acceleration

Q. The position vector of a particle changes with time according to the relation $\overrightarrow{r}\left(t\right)=15t^2\hat{i}+(4-20t^2)\hat{j}$. What is the magnitude of the acceleration at $t=1$?

1. $40$
2. $100$
3. $50$
4. $25$

Q. The value of acceleration due to gravity is $g_1$ at a height $h=\frac{R}{2}$ ($R=$ radius of the earth) from the surface of the earth. It is again equal to $g_1$ and a depth $d$ below the surface. The ratio $\left(\frac{d}{R}\right)$ equals

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

Q. A particle of mass $2\text{kg}$ initially at origin $(0,0)$ moves with an initial velocity $\overrightarrow{V}=4\hat{i}+4\hat{j}\text{m/s}$. If a constant force $\overrightarrow{F}=-20\hat{j}\text{N}$ is applied on the particle, the $x-$coordinate of the particle when its $y-$coordinate again becomes zero is

1. $1.2\text{m}$
2. $4.0\text{m}$
3. $6\text{m}$
4. $3.2\text{m}$

Q. Position vector of a particle is given as $\overrightarrow{r}=(\frac{4}{3}{t}^{\frac{3}{2}}\hat{i}-\frac{t^2}{2}\hat{j}+2t\hat{k})m$. Magnitude of acceleration at $t=1\text{sec}$ is:

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

Q. why does the positive value of acceleration must not be speeding up for a particle in one -dimension motion ?explain with an example

Q. Velocity of a particle moving along x-axis is given as $v=t^2-4t$

1. Particle accelerates for $0\le t<2$
2. Particle accelerates for $2\le t\le 4$
3. Maximum speed attained by the body between 0 to 4 sec is 4 m/s
4. Particle retards for $2<t\le 4$

Q. A particle is moving along the $x-$axis, with its coordinate with time ${}^{\prime }{t}^{\prime }$ given by $x\left(t\right)=10+8t-3t^2$. Another particle is moving along the $y-$axis, with its coordinate as a function of time given by $y\left(t\right)=5-8t^3$. At $t=1\text{s}$, the speed of the second particle as measured in the frame of the first particle is given as $\sqrt{v}$. Then $v$ $\text{(in m/s)}$ is

Q. Two particles of equal masses have initial velocities $2\hat{i}{\text{ms}}^{-1}\text{and}2\hat{j}{\text{ms}}^{-1}$. First particle has a constant acceleration of $(\hat{i}+\hat{j}){\text{ms}}^{-2}$ while the acceleration of the second particle is always zero. The centre of mass of the two particles moves in a,

1. Circle
2. parabola
3. Ellipse
4. Straight line

Q. A particle of mass $1\text{kg}$ is projected with a speed of $10\text{m/s}$ in a uniform gravitational field as shown in the figure. The trajectory of the particle is given by

1. $9x=24y+y^2$
2. $18x=24y+5y^2$
3. $18x=12y+10y^2$
4. $36x=24y-5y^2$

Q. A body moving in a circular track covers equal distances in equal intervals of time. The body has

1. uniform velocity.
2. varying speed.
3. uniform acceleration.
4. uniform speed and acceleration of fixed magnitude.

Q. A particle moves in a circle of radius 50cm with a constant speed of 5m/s. Its acceleration is

Q. Find the relation between the acceleration of sphere $\left(a\right)$ and acceleration of wedge $\left(b\right)$ in the figure shown

1. $a=\frac{b\cos \alpha }{\cos \beta }$
2. $a=\frac{b\cos \beta }{\cos \alpha }$
3. $a=\frac{b{\cos }^2\beta }{\sin \alpha }$
4. $a=\frac{b{\sin }^2\beta }{\cos \alpha }$

Q.

So in 2D motion does the instantaneous acceleration always have to be along the same line as velocity( either 0 or 180 degrees)?

1. In 2D acceleration will not be a vector

2. Yes, It has to be either at 0 or 180 degree to the velocity

3. It can also be perpendicular to velocity but not any other angle

4. It can point in any arbitrary direction

Q.

A particle is moving along the curve $x=a{t}^2+bt+c$. If $ac=b^2$, then the particle would be moving with uniform

1. Rotation

2. Velocity

3. Acceleration

4. Retardation

Q. A car starts from rest and moves along the x-axis with constant acceleration $5m{s}^{-2}$ for 8 seconds. If it then continues with constant velocity, what distance will the car cover in 12 seconds since it started from rest?

1. 320 m
2. 160 m
3. 480 m
4. 720 m

Q. ntA particle moves in a circle of radius 25cm at 2 revolutions per second . The acceleration of the particle is ( in m/second square)n

Q.

A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s⁻¹ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.

Q.

The position of a body moving along the x-axis at time t is given by $t^2-4t+6$. The distance traveled by body in time interval t= 0 to t = 3 s is

1. $5m$
2. $7m$
3. $4m$
4. $3m$

Q. A particle moves such that its x and y coordinates as a function of time are x = 2+ $5t^2$ and y = $t^3$. Acceleration of particle at t = 2 sec is

1. 
   12 m/$s^2$
2. 
   $\sqrt{244}$ m/$s^2$
3. 
   $\sqrt{136}$ m/$s^2$
4. 
   0 m/$s^2$

Q.

A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s⁻¹ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.

Q. A body revolves with a constant speed V in a circular path of radius R. What is the magnitude of its average acceleration during motion between two points in diametrically opposite direction??

Q.

A plane flies 10 km east from city A to city B in 2 hrs and then 20 km south from city B to city C in 1 hr. For the total trip, what are the magnitude and direction of its average acceleration?

1. $\frac{-5}{3}\hat{i}-\frac{20}{3}\hat{j}$

2. $\frac{5}{3}\hat{i}-\frac{20}{3}\hat{j}$

3. $South-eastdirection$

4. $South-westdirection$

Q. If a rigid body rolls on a surface without slipping, then:

1. linear speed is maximum at the highest point but minimum at the point of contact
2. linear speed is minimum at highest point but maximum at the point of contact
3. linear speed is same at all points of the rigid body
4. angular speed is different at different points of a rigid body

Q. A sphere is rolling on a frictionless surface as shown in figure with a translational velocity $\nu m{s}^{-1}$. If sphere is to climb up the inclined surface, then $\nu$ should be

1. $2gh$
2. $\ge \sqrt{\frac{10}{7}gh}$
3. $\ge \sqrt{2gh}$
4. $\frac{10}{7}gh$

Q. A particle moves in a region with a uniform magnetic field and a parallel, uniform electric field. At some instant, the velocity of the particle is perpendicular to the field direction. The path of the particle will be
(a) a straight line
(b) a circle
(c) a helix with uniform pitch
(d) a helix with non-uniform pitch

Q. Given that for a two-dimensional motion, velocity $\overrightarrow{v}=t\hat{i}+t^2\hat{j}$. If particle starts from $(0,0)$ then find out the magnitude of displacement in next $2\text{seconds}$.

1. $\frac{10}{3}\text{m}$
2. $\frac{5}{3}\text{m}$
3. $\frac{7}{9}\text{m}$
4. $\frac{8}{3}\text{m}$

Q. Find out the centre of mass of a system of three particles of $1kg,2kg,3kg$ respectively kept at the vertices of an equilateral triangle of side $1m$ as shown.

1. $\frac{2}{3}m$, $\frac{\sqrt{3}}{6}m$
2. $\frac{5}{3}m$, $\frac{\sqrt{5}}{6}m$
3. $\frac{2}{3}m$, $\frac{\sqrt{8}}{6}m$
4. $\frac{4}{3}m$, $\frac{\sqrt{4}}{6}m$

Q. Find the torque $(\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F})$ of a force $\overrightarrow{F}=-3\hat{j}+5\hat{k}$ acting at the point $\overrightarrow{r}=7\hat{i}+3\hat{j}+\hat{k}$.

1. $-14\hat{i}+38\hat{j}+16\hat{k}$
2. $4\hat{i}+4\hat{j}+6\hat{k}$
3. $-14\hat{i}+38\hat{j}-16\hat{k}$
4. $18\hat{i}-35\hat{j}-21\hat{k}$

Q.

A lorry is going north at 10 m/s and then takes a curved road and is now going east at 10 m/s. This took 10 secs. What's the average acceleration during this time?

1. √2 m/s² NE

2. 10 m/s²

3. Zero

4. √2 m/s² SE

Q.

A plane flies 10 km east from city A to city B in 2 hrs and then 20 km south from city B to city C in 1 hr. For the total trip, what are the magnitude and direction of its average acceleration?

1. 

2. 

3. 

4.