If the position of a moving particle, with respect to time be, x(t) = 1 + t − t², then, the acceleration of particle is given by (assume all measurements in MKS)

• − 1 ms^-2

• − 1.5 ms^-2

• − 2 ms^-2

• − 2.5 ms^-2

A ball is dropped from a tower of height h. The duration (t₀) of motion, when it reaches bottom of the tower is given by

• $\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}}$

• $\sqrt{\frac{\mathrm{h}}{\mathrm{g}}}$

• $2 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}$

• $4\sqrt{\frac{\mathrm{h}}{\mathrm{g}}}$

For the given position-time (x − t) graph , the interval in  which velocity is zero, is

• (t₃ − t₁)

• (t₃ − t₂)

• (t₅ − t₄)

• (t₅ − t₂)

A particle moves along the x-axis as x = u (t −2s) + a (t − 2s)². The initial velocity of the particle is

• u − 2a

• u − 4a

• 2a − u

• 2a − 3u

185.

A small ball released from rest from a height h on a smooth surface of varying inclination, as shown in figure.

The speed of the ball when it reaches the horizontal part of the surface is

• ${\mathrm{v}}_0 = \sqrt{\mathrm{gh}}$

• ${\mathrm{v}}_0 = \sqrt{5\mathrm{gh}}$

• ${\mathrm{v}}_0 = \sqrt{2\mathrm{gh}}$

• None of these

Two masses m₁ = 5 kg and m₂ = 4.8 kg tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift is free to move ?

• 0.2 m/s²

• 9.8 m/s²

• 5 m/s²

• 4.8 m/s²

A person travelling on a straight line moves with an uniform velocity v₁ for some time and with uniform velocity v₂ for the next equal interval of time. The average velocity for the entire duration is

• ( v₁ + v₂ )

• (v₁ + v₂ ) / 2

• (v₁ + v₂ ) / 3

• (2v₁ + 3v₂ ) / 3 

If a particle moves a distance x at a speed v₁ and comes back with speed v₂ , then the average speed and average velocity during this round trip will respectively be

• 0, v₁ + v₂

• $\frac{2{\mathrm{v}}_1{\mathrm{v}}_2}{{\mathrm{v}}_1 + {\mathrm{v}}_2}, 0$

• v₁ + v₂, 0

• v₁ − v₂, $\frac{2{\mathrm{v}}_1{\mathrm{v}}_2}{{\mathrm{v}}_1 + {\mathrm{v}}_2 }$

A metal block of mass 1 kg is resting on a frictionless horizontal plane. It is struck by a jet releasing water at a rate of 1 m/s and at a speed of 4 m/s. Then, the initial acceleration of the block will be

• 2 m/s²

• 8 m/s²

• 1 m/s²

• 4 m/s²

A monkey of mass 30 kg climbs on a massless rope whose breaking strength is 450 N. The rope will break if the monkey (Take g = 10 m/s² )

• climbs up with a uniform speed of 5 m/s

• climbs down with an acceleration 4 m/s²

• climbs up with an acceleration 6 m/s²

• climbs down with a uniform speed of 5 m/s²