The displacement x of a particle along a straight line at time t is given by $\mathrm{x}={\mathrm{a}}_0+{\mathrm{a}}_1\mathrm{t}+{\mathrm{a}}_2{\mathrm{t}}^2$. The acceleration of the particle is:
1. \(a_0\)
2. \(a_1\)
3. \(2a_2\)
4. \(a_2\)

The area \(A\) of a metallic disc (in square metres) varies with time \(t\) (in seconds) according to the equation: \(A=5t^2+2t.\)
What is the rate of change of the area with respect to time at \(t=3 ~\text s\text{?}\)

The current in a circuit is given by: \(I=\dfrac{dq}{dt}.\) If the charge flowing through the circuit is described by: \(q=(t^2-3t+4),\) at what time is the current in the circuit equal to zero?
1. \(t=3\) s
2. \(t=2\) s
3. \(t=1.5\) s
4. \(t=15\) s

A particle moves along the X-axis so that its X coordinate varies with time t according to the equation $\mathrm{x}=\left(2-5\mathrm{t}+6{\mathrm{t}}^2\right)\mathrm{m}$. The initial velocity of the particle is: \(\left(\text{Given;}~ v=\frac{dx}{dt}\right)\)
1. -5 m/s
2. 6 m/s
3. 3 m/s
4. 4 m/s

A body is moving according to the equation \(x = at +bt^2-ct^3\) where \(x\) represents displacement and \(a, b~\text{and}~c\) are constants. The acceleration of the body is: (\(\text{Given:}~ a=\frac{d^2x}{dt^2}\))
1. \(a+ 2bt\)
2. \(2b+ 6ct\)
3. \(2b- 6ct\)
4. \(3b- 6ct^2\)

If \(y = t^3+1\) and \(x = t^2+3,\) what is the value of \(\dfrac{dy}{dx}?\)
1. \(\dfrac{t^2}{3}\)
2. \(\dfrac{t}{2}\)
3. \(\dfrac{3t}{2}\)
4. \(t^2\)

The position \(x\) of the particle varies with time \(t\) as \(x = at^2-bt^3\)${\mathrm{}}^{}$.  The acceleration of the particle will be zero at a time equal to: \(\left(\text{Given:}~ a=\frac{d^2x}{dt^2}\right)\)
1. \(\frac{a}{b}\)
2. \(\frac{2a}{b}\)
3. \(\frac{a}{3b}\)
4. zero