Magnitude and Direction of Acceleration

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. 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.

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

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

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

3. In 2D acceleration will not be a vector

4. It can point in any arbitrary direction

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. 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.

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.

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. $\sqrt{2}m/s^{2}NE$

2. $10m/s^2$

3. $Zero$

4. $\sqrt{}2m/s^{2}SE$

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