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A particle moving with an initial velocity $i^−4j^ +10k^$ has acceleration $i^+j^ −2k^$. Its velocity at the end of 2 seconds, points along the unit vector:

A particle moves in XY plane according to the law $x$ = $asin(t)$ and $y$ = $a(1−cos(t))$ where a is constant. The particle traces :

Which of the following displacement $(x)$ vs. time $(t)$ graphs is not possible?

A man is going in a topless car with a velocity of $10.8km/h$. It is raining vertically downwards. He has to hold the umbrella at an angle of $53_{o}$ to the vertical to protect himself from rain. The actual speed of the rain is $(cos53_{o}=53 )$

Consider the following statements A and B and identify the correct answer.

A) The speed acquired by a body when falling in a vacuum for a given time is dependent on the mass of the falling body.

B) A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion. The stone remains in the air for $5s$. [$g=10ms_{−2}$]

A) The speed acquired by a body when falling in a vacuum for a given time is dependent on the mass of the falling body.

B) A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion. The stone remains in the air for $5s$. [$g=10ms_{−2}$]

A body starts from rest and moves with an uniform acceleration. The ratio of distance covered in the $n_{th}$ second to the distance covered in $n$ seconds is :

Raindrops are falling vertically with a velocity $10m/s$. To a cyclist moving on a straight road the raindrops appear to be coming with a velocity of $20m/s$. The velocity of cyclist is

A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity vs time?

A ball is dropped vertically from height $h$ and is bouncing elastically on the floor (see figure). Which of the following plots best depicts the acceleration of the ball as a function of time.

Position (Km) - Time (min.) graph is as shown for two cars $A$ and $B$. Both collide at time $t=150$ minute. Then the distance of position $R$ of accident from the starting point $Q$ of car $A$ will be: (Initial distance between the two cars is $500$ km) (Position in the graph shows the distance of the two cars from the point $Q$)