$A$ particle is moving in a straight line. Its displacement at time $t$ is given by $s = -4t^2 + 2t$. Then its velocity and acceleration at time $t = \frac{1}{2} \text{ s}$ are:

The diameter and altitude of a right circular cone,at a certain instant,were found to be $10 \ cm$ and $20 \ cm$ respectively. If its diameter is increasing at a rate of $2 \ cm/s$,then at what rate must its altitude change,in order to keep its volume constant (in $cm/s$)?

If a man of height $1.8 \ m$ is walking away from the foot of a light pole of height $6 \ m$ with a speed of $7 \ km/h$ on a straight horizontal road,then the rate of change of the length of his shadow is (in $km/h$):

The relation between pressure $p$ and volume $V$ is given by $p V^{1/4} = \text{constant}$. If the percentage decrease in volume is $\frac{1}{2} \%$,then the percentage increase in pressure is:

If the radius of a circular blot of oil is increasing at the rate of $2 \text{ cm/min}$,then the rate of change of its area when its radius is $3 \text{ cm}$ is:

The surface area of a cube increases at a rate of $2 \ cm^2/sec$. The rate at which its volume increases when the length of its edge is $90 \ cm$ is ..... $cm^3/sec$.