Questions tagged 'Application of Derivatives'

• A particle moves in a straight line in such a way that its velocity at any point is given by ${{v}^{2}}=2-3x$ , where x is measured from a fixed point. The acceleration is
  Category: differentiation | Tags: Application of Derivatives
• A stone is falling freely and describes a distance s in t seconds given by equation $s=\frac{1}{2}g\,{{t}^{2}}$ . The acceleration of the stone is
  Category: differentiation | Tags: Application of Derivatives
• The radius of a sphere is measured to be 20 cm with a possible error of 0.02 of a cm. The consequent error in the surface of the sphere is
  Category: differentiation | Tags: Application of Derivatives
• The displacement of a particle in time t is given by $s=2{{t}^{2}}-3t+1$ . The acceleration is
  Category: differentiation | Tags: Application of Derivatives
• The equation of motion of a particle is given by $s=2{{t}^{3}}-9{{t}^{2}}+12t+1$ ,where s and t are measured in cm and sec. The time when the particle stops momentarily is
  Category: differentiation | Tags: Application of Derivatives
• If a spherical balloon has a variable diameter $3x+\frac{9}{2}$ , then the rate of change of its volume with respect to x is
  Category: differentiation | Tags: Application of Derivatives
• The velocity of a particle at time t is given by the relation $v=6t-\frac{{{t}^{2}}}{6}$ . The distance traveled in 3 seconds is, if $s=0$ at $t=0$
  Category: differentiation | Tags: Application of Derivatives
• The equation of motion of a car is $s={{t}^{2}}-2t$ , where t is measured in hours and s in kilometers. When the distance travelled by the car is $15\,km$ , the velocity of the car is
  Category: differentiation | Tags: Application of Derivatives
• A stone moving vertically upwards has its equation of motion $s=490t-4.9{{t}^{2}}$ . The maximum height reached by the stone is
  Category: differentiation | Tags: Application of Derivatives
• The edge of a cube is increasing at the rate of $5cm/\sec .$ How fast is the volume of the cube increasing when the edge is 12cm long
  Category: differentiation | Tags: Application of Derivatives

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