A 0.2 kg object at rest is subjected to a force  $\left(0.3 \hat{\mathrm{i}} - 0.4 \hat{\mathrm{j}}\right)$N. What is the velocity after 6 s?

• $\left( 9 \hat{\mathrm{i}} - 12 \hat{\mathrm{j}} \right)$

• $\left( 8 \hat{\mathrm{i}} - 16 \hat{\mathrm{j}} \right)$

• $\left(12 \hat{\mathrm{i}} - 9 \hat{\mathrm{j}} \right)$

• $\left( 16 \hat{\mathrm{i}} - 8 \hat{\mathrm{j}} \right)$

If man were standing unsymmetrically between parallel cliffs, claps his hands and starts hearing a series of echoes at intervals of 1 s. If speed of sound in air is 340 ms', the distance between two cliffs would be

• 340 m

• 510 m

• 170 m

• 680 m

Half life of a radioactive material is 5 years, then the percentage of it remained after 25 years will be

• 3.125%

• 6.25%

• 1.25%

• 25%

The position of a particle moving in the x-y plane at any time t is given by; x = ( 3t³ $-$ 6t ) meters;  y = ( t² - 2t) meters. Select the correct statement.

• acceleration  is  zero  at  t = 0

• velocity  is  zero  at  t = 0

• velocity  is  zero  at  t = 1s

• velocity  and  acceleration of the particle are never zero

Assertion:  A horse has to pull a cart harder during the first few steps of his motion. 

Reason: The first few steps are always difficult.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Two masses  M₁ = 5 kg  and  M₂ =  10 kg  are  connected at the ends of an inextensible string  passing  over  a frictionless  pulley  as  shown. When  the  masses  are  released, then  the  acceleration  of  the  masses  will  be

• g

• g/2

• g/3

• g/4

157.

The displacement time graph of a particle moving along a straight line is drawn below.

 

The accelerations of the particle during the regions  OP, PQ  and  QR

• OP	PQ	QR
  -	0	+

• OP	PQ	QR
  +	0	+

• OP	PQ	QR
  +	0	-

• OP	PQ	QR
  -	+	-

The curve between log_e  $\frac{\mathrm{J}}{{\mathrm{T}}^2}$  and  $\frac{1}{\mathrm{T}}$ is

Which of the following velocity-time graphs shows a realistic situation for a body in motion?

Two spheres of same size, one of mass 2 kg and another of mass 4 kg are dropped simultaneously from the top of Qutab Minar  ( height ≈ 72 m ). When they are 1 m  above the ground the two spheres have the same

• momentum

• kinetic energy

• potential energy

• acceleration