Motion In Straight Line

The distance travelled by a particle starting from rest and moving with an acceleration (4/3)ms⁻², in the 3rd second is

What will be the ratio of the distance moved by a freely falling body from rest in 4th and 5th seconds of journey?

The displacement of particle is given by x=aₒ+(a₁t/2)-(a₂t²/3) what is acceleration?

A car accelerates from rest at constant rate for first 10s at the same acceleration. Which of the following is true?

A particle is released from rest from a tower of height 3h, the ratio of time of fall for equal heights h (t₁ : t₂ : t₃ is)

An aeroplane flies 400m due to North and then 300m due to south and then flies 1200m upwards, the net displacement is

A bullet loses 1/20 of its velocity after penetrating a plank.How many planks are required to stop the bullet

A particle moves a distance x in time but according to equation x=(t+5)⁻¹. The acceleration of particle is proportional to

A ship A is moving westwards with a speed of 10 km/h and ship B located 100 km south of A is moving Northwards with a speed of 10km/h.The time after which the distance between them becomes shortest, is

A boy standing at top of a tower of 20 m height drops a stone. Assuming g=10 ms⁻², the velocity with which it hits the ground is

A particle covers half of its total distance with speed v1 and the rest half distance with speed v2.  Its average speed during the complete journey is

A stone falls freely under gravity.  It covers distances h1, h2 and h3 in the first 5 seconds,the next 5 seconds and the next 5 seconds respectively. The relation between h1, h2 and h3 is

A boat taken 2 h to travel 8 km and back in still water. If the velocity of water 4 km/h, the time for going up stream 8 km and coming back is

The velocity of a particle at an instant is 10 ms⁻¹. After 3s its velocity will become 16 ms⁻¹. The velocity at 2s before the given instant, will be

A particle is dropped vertically from rest, from a height.The time taken by it to fall through successive distances of 1m each will be, then

A ball rolls off the top of stair way with a horizontal velocity of magnitude 1.8 m/s. The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first?

Two bodies A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is

A ball is dropped into a well in which the water level is at a depth h below the top. If the speed of sound is c, then the time after which the splash is heard will be given by

A particle moves along the x-axis such that its co-ordinate (x) varies with time (t), according to the expression x = 2- 5t + 6t², where x is in metre and t is in second. The initial velocity of the particle is

A body is thrown vertically upward in air when air resistance is taken into account,the time of ascent is t₁ and time of descent is t₂, then which of the following is true?

A boat which has a speed of 5 kmh⁻¹ in still water crosses river of width 1 km along the shortest path in 15 min. The width of the river in kmh⁻¹ is

A particle moves along with x-axis. The position x of particle with respect to time t from origin is given by x=bₒ+b₁t+b₂t². The acceleration of particle is

A particle moving in a straight line covers half the distance with speed of 3 ms⁻¹. The other half of the distance is covered in two equal time intervals with speed of 4.5 ms⁻¹ and 7.5 ms⁻¹, respectively. The average speed of the particle during this motion is

A body travelling along a straight line traversed one-third of the total distance with a velocity 4 ms⁻¹. The remaining part of the distance was covered with a velocity 2 ms⁻¹ for half the time and with velocity 6 ms⁻¹ for the other half time. The average velocity over the whole time of the motion is

A body is thrown vertically up with a velocity u. It passes three points A, B and C in its upward journey with velocity u/2, u/3 and u/4, respectively.  The ratio of separations between points AB and between BC, i.e, AB/BC is

A particle moving along x-axis has acceleration f, at time t, given by f=f₀(1-t/T), where f₀ and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle’s velocity is

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x)=βx⁻²ⁿ where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by

When a ball is thrown up vertically with velocity vₒ, it reaches a maximum height of h. If one wishes to triple the maximum height, then the ball should be thrown with velocity

The displacement ‘x’ (in meter) of a particle of mass ‘m’ (in kg) moving in one dimension under the action of a force, is related to time ‘t’ (in sec) by t = √x + 3. The displacement of the particle when its velocity is zero, will be

A particle moving along a straight line OX. At a time (in second ) the distance x (in metre) of the particle from O is given by x=40+12 t-t³. How long would the particle travel before coming to rest?

A ballon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height h. The time taken by the stone to reach the ground is

The velocity of a particle at an instant is 10 ms⁻¹ and after 5 s the velocity of the particle is 20 ms⁻¹. The velocity 3 s before in ms⁻¹ was

A 120 m long train is moving in a direction with speed 20 m/s. A train B moving with 30 m/s in the opposite direction and 130 m long crosses the first train in a time

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 s. What should be the speed of the throw, so that more than two balls are in the sky at any time? (take,g=9.8 ms⁻²)

A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km/h. The jeep follows it at a speed of 90 km/h, crossing the turning 10 s later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike? (in km)

The position x of a particle with respect to time t along X-axis is given by x=9t²-t³, where x is in metre and t in second. What will be the position of this particle when it achieves maximum speed along the +x direction?

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S₁ and that covered in the first 20 seconds is S₂, then:

A particle moving in a straight line with uniform acceleration is observed to be a distance a from a fixed point initially. It is at distance b, c, d from the same point after n, 2n, 3n seconds. The acceleration of the particle is

A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v.The two balls meet at t = 18s. What is the value of v?(take g = 10 m/s²)

The motion of a particle along a straight line is described by equation : x= 8 + 12t – t³ where x is in metre and t in second. The retardation of the particle when its velocity becomes zero, is :

Water drops fall from a top on the floor 5 m below at regular intervals. If time, the first drop striking the floor when the fifth drop begins to fall. The height at which the third drop will be from ground (at the instant when the first drop strikes the ground) will be (take, g=10 ms²)

An elevator car whose floor to ceiling distance is equal to 2.7 m starts ascending with constant acceleration of 1.2 ms⁻². After 2s of the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is

A dust packet is dropped from 5th storey of a multi-storeyed building. In the first second of its free fall another dust packet is dropped from 7th storey 15 m below the 9th storey. If both packets reach the ground at same time,then height of the building is

At a metro station, a girl walks up a stationary escalator in time t₁. If she remains stationary on the escalator, then the escalator take her up in time t₂. The time taken by her to walk up on a moving escalator will be

A juggler maintains four balls in motion, making each of them to rise a height of 20 m from his hand. What time interval should be maintained for the proper distance between them? (take,g=10 ms⁻²)

A body initially at rest is moving with uniform acceleration a m/s². It’s velocity after n second is v. The displacement of the body in last 2s is

A train is moving along a straight path with uniform acceleration. It’s engine passes across a pole with a velocity of 60 kmh⁻¹ and the end (guard’s van) passes across same pole with a velocity of 80 kmh⁻¹. The middle point of the train will pass across same pole with a velocity

A body starts from rest, what is the ratio of the distance travelled by the body during the 4th second and 3rd second?

A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms⁻¹ to 20 ms⁻¹ while passing through a distance 135m in t second. The value of t is:

A bus is moving with a speed of 10 ms⁻¹ on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?