A body is moving in a circular path of radius ‘r’, then, displacement and distance travelled by body when angular displacement is 90^o is

The displacement of a body from a fixed point at any instant is given by [latex]x = 5t^2 + 6t + 4[/latex], what type of motion the particle undergoes?

The horizontal range of projectile is [latex]4\sqrt{3}[/latex] times maximum height, the angle of projectile is

Which of the following represent maximum horizontal distance

The acceleration of a particle can be found from

Initial velocity of a body is 5m/s whose acceleration is [latex]10\ m/s^2[/latex]. What is the distance covered in 10 second.

A body starts from the rest falls vertically through a height of 20 m. If g = [latex]10\ m/s^2[/latex], the time taken by body to fall through the last 2 meters of falls.

A ball is thrown horizontally with a velocity u from a tower of height h. Then, horizontal range will be

The distance travelled by a body falling freely from rest in first, second and third second are in ratio

A ball is released from the top of a tower of height H. It takes T second to reach ground. What is the time required to reach half of tower (H/2)

A body falls freely from the top of a tower and it falls [latex](\frac{7}{16})^{th}[/latex] of total distance in its last second. The time taken by body to complete motion is

A balloon is going up at steady velocity of [latex]20ms^{-1}[/latex]. When it was 60m above ground, an object is dropped from it. How long does the object take to reach ground

A man goes to his office from home at the speed of [latex]v_1[/latex] and return next half distance with velocity [latex]v_2[/latex]. The average velocity of the car is

A motorcyclist travels along a straight line for first half time with speed [latex]v_1[/latex] and second half time with speed [latex]v_2[/latex]. The average speed is

Numerical ratio of displacement to distance is

A stone is dropped into a well in which level of water is h below the top of well. If v be the speed of sound. The time T after which the splash is heard is given by

From a flying aeroplane a body should be dropped in advance to hit the target, why?

A ball is dropped gently from the top of a tower and another ball is thrown horizontally at the same time. Which ball will hit the ground first?

Can an object with constant acceleration reverse its direction? Explain.

Velocities of two bodies A and B are given in vector notation as  and  respectively. What will be the relative velocity of B with respect to A in this notation? 

Two stones P and Q of different masses m and 2m respectively are dropped simultaneously from the top of a tower and reach the ground with different energies. Which one is faster?

From a high tower, one ball is dropped from rest and the second ball is simultaneously projected horizontally. Neglecting air resistance, which ball will reach the ground earlier?

A ball is thrown with a velocity v at an angle  with the horizontal. Can another angle of projection achieve the same horizontal range? Justify your answer.

Rain drops hitting the side windows of a car, in motion often leave diagonal streaks. Why?

If the displacement of body is proportional to square of time, state whether the body is moving with uniform velocity or uniform acceleration.

A bomb is to be dropped from a moving helicopter on a target on the ground. Explain how it can hit the target.

Can you have a zero acceleration but non-zero velocity? Explain with help of a graph.

A projectile move in a parabolic path without air resistance. Is there any point at which its acceleration is perpendicular to the velocity? Explain.

Angle between the velocities  and  of two bodies A and B is . Explain, with figure, the difference between the relative velocity of
i. A with respect to B and
ii. B with respect to A.

Can the direction of the velocity of a body be changed when its acceleration is constant?

Can a body have a constant spaced but changing velocity? Explain with example.

When a rifle is fired at a distant target, the barrel is not lined up exactly on the target. Why not? Does the angle of projection depend on the distance of the target?

A swimmer wants to reach to a point just opposite on the other bank of the river. How should he swim and why?

A package is dropped out of an aeroplane in a level flight. If air resistance is neglected, how would the motion of the package look to the pilot?

A body is thrown vertically upwards from the ground with a velocity v. It reaches the maximum height and returns to the ground. The same body is projected with the same velocity but making an angle 30° with the horizontal. In which case the body remains in air for longer duration? Explain.

A motor cycle is moving with v towards east and crosses a bicyclist coming with a velocity v from north-east direction. How will you find the relative velocity of motor cycle with respect to the bicyclist?

Find the angle of projection at which the horizontal range and maximum height of a projectile are equal.

What would be the effect on maximum range in doubling the initial velocity of a projectile?

Can an object have an eastward velocity experiencing a westward acceleration? Give reasons.

A car is moving on the road when the rain is falling vertically downwards. Why does the front wind screen get wet?

A projectile fired at an angle of 18° has certain horizontal range. State another angle of projection for the same horizontal range.

Give with an example a case where the velocity of an object is zero but its acceleration is not zero.

Because of air resistance two objects of unequal mass do not fall at precisely the same rate. If two bodies of identical shape but unequal mass are dropped simultaneously from the same height, which one reaches the ground first?

A stone is projected with a velocity in a direction making an angle [latex]\theta with horizontal. Derive expression for: (i) maximum height (ii) time of flight (iii) horizontal range. Also find the condition for maximum horizontal range. [3]

Show that path followed by a projectile fired at an angle [latex]\theta with horizontal is a parabola. Assuming that the point of projection and the landing point are at the same horizontal level. Find the expression for horizontal range. [3]

Define projectile. Show that the path of projectile projected horizontally from the top of tower is parabolic. At what angle does it hit on the ground? [3]

A swimmer’s speed along the river (downstream) is 20 Km/h and can swim upstream at 8 km/h. calculate the velocity of the stream and the swimmer’s possible speed in still water. [3] Ans: 14 km/h, 6 km/h

A body is projected upwards making an angle [latex]\theta[/latex] with the horizontal with a velocity of 300 ms^-1. Find the value of [latex]\theta[/latex] so that the horizontal range will be maximum. Hence find its range and time of flight. [3] Ans: [latex]45^o[/latex], 9000 m, 42.43 s

A stone on the edge of a vertical cliff is kicked so that its initial velocity is 9 m/s horizontally. If the cliff is 200 m high, calculate:
i.    Time taken by stone to reach the ground.
ii.   How far from the cliff the stone will hit the ground? [3] Ans: 6.32 sec, 56.92 m

A projectile is fired from ground level with a velocity 500 m/s at 30^o to the horizontal. Find its horizontal range, the greatest height and the time to reach the greatest height. [3] Ans: 21650.63 m, 3125 m, 25 s

A batter hits a baseball so that it leaves the bat with an initial speed 37 m/s at an angle of 53^o, find the position of the ball and the magnitude and direction of its velocity after 2 seconds. Treat the baseball as a projectile. [3] Ans: 24.228 m/s, 23.21^o

A baseball is thrown towards a player with an initial velocity 20 ms^-1 and 45^o with the horizontal. At the moment, the ball is thrown the player is 50 m from the thrower. At what speed and in what direction must he run to catch the ball at the same height at which it is released? [3] Ans: [latex]3.53\ ms^{-1}[/latex] towards the thrower

An airplane is flying with a velocity of 90.0 m/s at an angle of 23.0^o above the horizontal. When the plane is 114 m directly above a dog that is standing on level ground, a suitcase drops out of luggage compartment. How far from the dog will the suitcase land? You can ignore air resistance. [3] Ans: 782 m

A bullet is fired with a velocity of 100 m/s from the ground at an angle of 60^o with the horizontal. Calculate the horizontal range covered by the bullet. Also calculate the maximum height attained. [3] Ans: 866m, 375m

A car travelling with a speed of 15 m/s is braked and it slows down with uniform retardation. It covers a distance of 88 m as its velocity reduces to 7 m/s. If the car continues to slow down with same rate, after what further distance will it be brought to rest? [3] Ans: 24.5 m

A stone is projected horizontally with 20 m/s from the top of a tall building. Calculate its position and velocity after 3 sec neglecting the air resistance. [3] Ans: 36 m/s, 56.3^o with horizontal

An object with mass m moves along the x – axis. Its position as a function of time is given by x(t) = At – Bt³, where A and B are constants. Calculate the net force on the object as a function of time. [2] Ans: 6 Bmt

A man wishes to swim across a river 600 m wide. If he can swim at the rate of 4 km/h in still water and the river flows at 2 km/h. Then in what direction must he swim to reach a point exactly opposite to the starting point and when will he reach it? [3] Ans: 120^o, 623.5 s, 120^o with river current or 30^o with the direction perpendicular to river current

A body falls freely from the top of a tower and during the last second of its fall, it falls through 25 m. Find the height of tower. [3] Ans: 45 m

A projectile is launched with an initial velocity of 30 ms^-1 at an angle of 60^o above the horizontal. Calculate the magnitude and direction of its velocity 5s after launch. [3] Ans: 28.3 m/s and 57^o with horizontal

An airplane pilot wishes to fly due west. A wind of 80 km/hr is blowing towards the south. If the speed of the plane in still air is 320 km/hr, in which direction should the pilot head? What is the speed of the plane with respect to the ground? [3] Ans: 14.5^o North of West, 310 km/hr

A projectile is fired from the ground level with a velocity of 500 ms^-1 at 30^o to horizontal. Find the horizontal range, and greatest vertical height to which it rises. What is the least speed with which it could be projected in order to achieve the same horizontal range? [g = 10 N kg^-1]. [3] Ans: 21650.6 m, 3125 m, 465.3 ms^-1

An object is dropped from the top of the tower of height 156.8 m and at the same time another object is thrown vertically upward with the velocity of 78.1 ms^-1 from the foot of the tower, when and where the object meets? [3] Ans: 2 s, 20 m below the top

A body is projected horizontally from the top of a tower 100 m high with a velocity of 9.8 ms^-1. Find the velocity with which it hits the ground. [3] Ans: 45.8 ms^-1, 77.64^o with horizontal