Acceleration for Non Linear Motion

Q.

A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates (meters) of the rabbit's position as functions of time t (seconds) are given by

$x=-\frac{t^2}{2}+5t+20$
And $y=t^2-10t+30$

Find the acceleration at time t = 15 s?

1. 

2. 

3. 

4. 

Q. The position of a particle moving in the X-Y plane from origin at any time $t$ is given by $x=(3t^2-6t)$ m; $y=(t^2-2t)$ m, where $t$ is in seconds. Select the correct statement(s) about the moving particle from the following.

1. The acceleration of the particle is zero at $t=0$ second
2. The velocity of the particle is zero at $t=0$ second
3. The velocity of the particle is zero at $t=1$ second
4. The velocity and acceleration of the particle are never zero

Q.

The $x$ and $y$ coordinates of the particle at any time are $x=5t-2t^2$ and $y=10t$ respectively, where $x$ and $y$ are in meters and $t$ in seconds. The acceleration of the particle at $t=2s$ is

1. $5m/s^2$
2. $-4m/s^2$
3. $-8m/s^2$
4. $0m/s^2$

Q. Particles's position as a function of time is given by $x=-t^2+4t+4$. The maximum value of position co-ordinate of particle is:

Q.

A particle's position in the x-y plane varies as $x\left(t\right)=3t^3+4t^2,y\left(t\right)=16t^4+2$

Find the acceleration vector of the particle after 1 sec of start.

1. $18m/s^2\hat{i}+192m/s^2\hat{j}$

2. $3m/s^2\hat{i}+16m/s^2\hat{j}$

3. $26m/s^2\hat{i}+192m/s^2\hat{j}$

4. $7m/s^2\hat{i}+18m/s^2\hat{j}$

Q.

A particle's position in the x-y plane varies as $x\left(t\right)=3t^3+4t^2,y\left(t\right)=16t^4+2$

Find the acceleration vector of the particle after 1 sec of start.

1. 

2. 

3. 

4. 

Q.

A particle's position in the x-y plane varies as $x\left(t\right)=3t^3+4t^2,y\left(t\right)=16t^4+2$

Find the acceleration vector of the particle after 1 sec of start.

1. $18m/s^2\hat{i}+192m/s^2\hat{j}$

2. $3m/s^2\hat{i}+16m/s^2\hat{j}$

3. $26m/s^2\hat{i}+192m/s^2\hat{j}$

4. $7m/s^2\hat{i}+18m/s^2\hat{j}$

Q.

A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates (meters) of the rabbit's position as functions of time t (seconds) are given by

$x=-\frac{t^2}{2}+5t+20$
And $y=t^2-10t+30$

Find the acceleration at time t = 15 s?

1. $2\hat{i}-1\hat{j}$

2. $1\hat{i}+1\hat{j}$

3. $2\hat{i}+2\hat{j}$

4. $-1\hat{i}+2\hat{j}$