The work done by gravity exerting an acceleration of -10 m/${\mathrm{s}}^2$ for a 10 kg block down 5 m from its original position with no initial velocity is:

$({\mathrm{F}}_{\mathrm{grav}}=\mathrm{mass} \times \mathrm{acceleration} \mathrm{and} \mathrm{W}={\int }_{\mathrm{a}}^{\mathrm{b}}\mathrm{F}(\mathrm{x}\left)\mathrm{dx}\right)$

1. 250 J

2. 500 J

3. 100 J

4. 1000 J

Water flows into a container of 1000 L at a rate of (180+3t) gal/min for an hour, where t is measured in minutes. Find the amount of water that flows into the pool during the first 20 minutes.

1. 4000 gal

2. 2800 gal

3. 4200 gal

4. 3800 gal

If v(t)=3t-1 and x(2)=1, then the original position function is: 
Hint: $\left(v\left(t\right)=\frac{ds}{dt}\right)$

1. $\frac{3}{2}{t}^2-t-3$

2. $\frac{1}{2}{t}^2-t-3$

3. $\frac{3}{2}{t}^2-2t-3$

4. None of the above

The position of a particle is given by $s\left(t\right)=\frac{2t^2+1}{t+1.}$ Then, at t = 2, its velocity is :$\left(v_{inst}=\frac{ds}{dt}\right)$

1. $\frac{16}{3}$

2. $\frac{15}{9}$

3. $\frac{15}{3}$

4. None of these

If acceleration of a particle is given as a(t)=sin(t)+2t. Then the velocity of the particle will be:

(acceleration $\mathrm{a}=\frac{\mathrm{dv}}{\mathrm{dt}}$)

1. $-\cos \left(\mathrm{t}\right)+\frac{{\mathrm{t}}^2}{2}$

2. $-\sin \left(\mathrm{t}\right)+{\mathrm{t}}^2$

3. $-\cos \left(\mathrm{t}\right)+{\mathrm{t}}^2$

4. None of these

If x=3tan(t) and y=sec(t), then the value of $\frac{d^{2}y}{d{x}^2} at t=\frac{\mathrm{\pi }}{4}$ is:

1. 3

2. $\frac{1}{18\sqrt{2}}$

3. 1

4. 1/6

A particle's position as a function of time is given by $\mathrm{x}=-{\mathrm{t}}^2+6\mathrm{t}+3$. The maximum value of the position co-ordinate of the particle is:

1. 8

2. 12

3. 3

4. 6

The equation of position (x) of a particle is given by $x=(-3t^3+18t^2+5)m$. The maximum velocity of the particle is, if velocity is defined as $v=\frac{dx}{dt}$ :

1. +56 m/s

2. +46 m/s

3. +36 m/s

4. +26 m/s

The current in a circuit is defined as $I=\frac{dq}{dt}$. The charge (q) flowing through a circuit, as a function of time (t), is given by $q=5t^2-20t+3$. The minimum charge flows through the circuit at:

1. t=4 sec

2. t=2 sec

3. t= 6 sec

4. t=3 sec

Work done by a force (F) in displacing a body by dx is given by W=$\int F\left(x\right).dx$. If the force is given as a function of displacement (x) by $F\left(x\right)=(x^2-2x+1)N$, then work done by the force from x=0 to x=3 m is:

1. 3 J

2. 6 J

3. 9 J

4. 21 J