Application in Mechanics

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What is the acceleration of a particle moving in a straight line with velocity given by v = 2 - 3x, where x is measured from a fixed point?

Uniform acceleration (correct)

Non-uniform acceleration

Acceleration that varies with x

Zero acceleration

What is the acceleration of a point moving in a curve given by x = at, y = b sin at?

Constant acceleration (correct)

Acceleration that varies with the distance from the origin

Acceleration that varies with the distance from the x-axis

Acceleration that varies with the distance from the y-axis

A particle moves in a straight line with displacement given by x = a + bt - ct^2. What is its acceleration?

2b + 2c

b + c

2b - 2c (correct)

2b - c

A stone is thrown vertically upwards from the surface of the moon with an initial velocity of 24 m/s. What is its acceleration?

Uniform acceleration Signup and view all the answers

A particle moves in a curve given by x = at, y = bt^2. What is its acceleration at time t?

2b Signup and view all the answers

A particle moves in a straight line with the position given by s = 15t - 2t². What is its acceleration?

-4 m/s² Signup and view all the answers

A stone is thrown vertically upwards with an initial velocity of 37.8 cm/s. How long does it take to reach its maximum height?

3 s Signup and view all the answers

A point moves in a straight line according to the law s = 15t - 2t². What is its velocity at t = 2 s?

19 m/s Signup and view all the answers

A circle is increasing uniformly at the rate of 3 cm/s. What is the rate of increase of its area when the radius is 10 cm?

10π cm²/s Signup and view all the answers

A particle moves according to the equation s = at² + bt + 6, where t ≥ 0. If it comes to rest after 4 seconds, what is the value of a?

-1.5 m/s² Signup and view all the answers

What is the acceleration of a stone thrown vertically upwards, given that the equation of motion is s = 80t - 16t²?

8 m/s² Signup and view all the answers

A ball is thrown vertically upwards with an initial velocity of u m/s. If it takes 6 seconds to return to the ground, what is the initial velocity?

29.4 m/s Signup and view all the answers

A particle moves according to the equation s = at² + bt + c. What is the acceleration of the particle?

2a Signup and view all the answers

A particle moves along a curve x = at² + bt + c, where ac = b². What type of motion is exhibited by the particle?

Uniform acceleration Signup and view all the answers

Two stones are thrown vertically upwards simultaneously, with equations of motion s = 19.6t - 4.9t² and s = 9.8t - 4.9t² respectively. What is the ratio of the maximum heights attained by the two stones?

2:1 Signup and view all the answers

What is the acceleration of a particle moving in a straight line with velocity given by v = 2 - 3x?

Uniform acceleration Signup and view all the answers

A stone is thrown vertically upwards from the surface of the moon with an initial velocity of 24 m/s. What is its acceleration?

1.6 m/s² Signup and view all the answers

What is the definition of velocity of a moving particle?

Rate of change of displacement with respect to time Signup and view all the answers

A point moves in a straight line according to the law x = at² + bt + c. What is its acceleration?

Uniform acceleration Signup and view all the answers

What is the type of motion exhibited by a particle moving in a curve given by x = at, y = b sin at?

Projectile motion Signup and view all the answers

What is the expression for the instantaneous velocity of a particle?

Lim Δt → 0 (Δs / Δt) Signup and view all the answers

A particle moves according to the equation s = at² + bt + c. What is its velocity at time t?

v = 2at + b Signup and view all the answers

What is the acceleration of a particle if its velocity varies?

dv / dt Signup and view all the answers

A particle moves according to the equation s = t³ + 2t² + t. What is its velocity at t = 1 second?

8 cm/sec Signup and view all the answers

What is the unit of acceleration?

m/s² Signup and view all the answers

What is the rate of increase of the area of the circular ripples when the radius is 10 cm?

120 π cm²/sec Signup and view all the answers

If the edge of a cube increases at the rate of 60 cm per second, at what rate is the volume increasing when the edge is 90 cm?

1458000 cu cm per sec Signup and view all the answers

If a spherical balloon has a variable diameter 3x + 2, then the rate of change of its volume with respect to x is?

27 π (2x + 3)² Signup and view all the answers

Two cyclists start from the junction of two perpendicular roads, their velocities being 3v metres/minute and 4v metres/minute. The rate at which the two cyclists are separating is?

7v m/min Signup and view all the answers

If y = ∫x^2 dt, then the rate of change of y with respect to x when x = 1, is?

2 Signup and view all the answers

Application in Mechanics

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Questions and Answers

What is the acceleration of a particle moving in a straight line with velocity given by v = 2 - 3x, where x is measured from a fixed point?

What is the acceleration of a point moving in a curve given by x = at, y = b sin at?

A particle moves in a straight line with displacement given by x = a + bt - ct^2. What is its acceleration?

A stone is thrown vertically upwards from the surface of the moon with an initial velocity of 24 m/s. What is its acceleration?

A particle moves in a curve given by x = at, y = bt^2. What is its acceleration at time t?

A particle moves in a straight line with the position given by s = 15t - 2t². What is its acceleration?

A stone is thrown vertically upwards with an initial velocity of 37.8 cm/s. How long does it take to reach its maximum height?

A point moves in a straight line according to the law s = 15t - 2t². What is its velocity at t = 2 s?

A circle is increasing uniformly at the rate of 3 cm/s. What is the rate of increase of its area when the radius is 10 cm?

A particle moves according to the equation s = at² + bt + 6, where t ≥ 0. If it comes to rest after 4 seconds, what is the value of a?

What is the acceleration of a stone thrown vertically upwards, given that the equation of motion is s = 80t - 16t²?

A ball is thrown vertically upwards with an initial velocity of u m/s. If it takes 6 seconds to return to the ground, what is the initial velocity?

A particle moves according to the equation s = at² + bt + c. What is the acceleration of the particle?

A particle moves along a curve x = at² + bt + c, where ac = b². What type of motion is exhibited by the particle?

Two stones are thrown vertically upwards simultaneously, with equations of motion s = 19.6t - 4.9t² and s = 9.8t - 4.9t² respectively. What is the ratio of the maximum heights attained by the two stones?

What is the acceleration of a particle moving in a straight line with velocity given by v = 2 - 3x?

A stone is thrown vertically upwards from the surface of the moon with an initial velocity of 24 m/s. What is its acceleration?

What is the definition of velocity of a moving particle?

A point moves in a straight line according to the law x = at² + bt + c. What is its acceleration?

What is the type of motion exhibited by a particle moving in a curve given by x = at, y = b sin at?

What is the expression for the instantaneous velocity of a particle?

A particle moves according to the equation s = at² + bt + c. What is its velocity at time t?

What is the acceleration of a particle if its velocity varies?

A particle moves according to the equation s = t³ + 2t² + t. What is its velocity at t = 1 second?

What is the unit of acceleration?

What is the rate of increase of the area of the circular ripples when the radius is 10 cm?

If the edge of a cube increases at the rate of 60 cm per second, at what rate is the volume increasing when the edge is 90 cm?

If a spherical balloon has a variable diameter 3x + 2, then the rate of change of its volume with respect to x is?

Two cyclists start from the junction of two perpendicular roads, their velocities being 3v metres/minute and 4v metres/minute. The rate at which the two cyclists are separating is?

If y = ∫x^2 dt, then the rate of change of y with respect to x when x = 1, is?

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