Motion in a Straight Line Questions

The acceleration-time graph of a particle moving along x-axis is shown. If the particle starts with 3 m/s at t = 0, find velocity at t = 4 s.

A person is standing on a weighing machine and observes that the reading is 60 kg, then suddenly jumps upward and observes that reading goes to 70 kg. Then his maximum upward acceleration is

A particle is projected vertically upward from ground at t = 0 with some velocity. If the magnitude of displacement in 5th second and 9th second are equal then the magnitude of displacement of the particle in 10th second will be (g = 10 m/s²)

Instantaneous velocity of a particle moving in +x direction given as v = . At t = 0, particle starts from origin. Average velocity of the particle while moving between the two points P(x = 1) and Q(x = 3) is

A train 200 m long moving at constant acceleration crosses a bridge 800 m long. It enters the bridge with speed of 2 m/s and its rear end leaves it with a speed of 5 m/s. Time taken to cross the bridge is nearly

A body starts from rest and moves for n seconds with uniform acceleration a. Its velocity after n seconds is v. The displacement of the body in last 4 seconds is

A particle is moving in a straight line with some initial velocity such that its acceleration during three consecutive equal intervals of time are in the ratio 1 : 2 : 7. The distances covered in the first and third parts are p and q while time taken

A car is moving eastward with a speed of 54 km/h, while wind is blowing northwards with a speed of 36 km/h. A flag on the car will flutter in the direction

The position x of a particle varies with time t as x = ct² – bt³, where c and b are constants. The acceleration of the particle will be equal to zero when t is equal to (All quantities are in SI units)

The position-time graph for two cars A and B is given below, then the ratio of their velocities is

If the time taken by a person to cover a circular path of radius 2 m is π s, then the angular velocity of the person in 1 complete rotation is

The ratio of magnitude of displacement to the distance covered is

Two trains each 100 m long are travelling in opposite direction with velocity 20 m/s and 30 m/s. Time taken by trains in crossing each other will be (in second)

The position-time graph of a moving particle is shown in graph. The instantaneous velocity of the particle is negative at the point

A particle is moving along x-axis. Its position (x) varies with time (t) as x = 4 + 2t – t²; where x is in meter and t is in second. At what time (t) it will reverse its motion?

A person travels along a straight road for the first time with a speed v₁ and for next time with a speed v₂. Then the mean speed v is given by

A particle moving along a straight line such that its velocity varies as v = 4t + 2. Distance covered by this particle in 6th second is [where v is in m/s and t is in s]

A car moving along a straight line with speed 72 km/h is brought to rest travelling a distance of 20 m. If retardation is uniform, then time taken (in s) to stop this car will be

Position of a particle varies with time (t) as x = . The acceleration of the particle is proportional to

A particle moving along North is subjected to a constant force resulting in an acceleration along North-east. The trajectory of the particle

If a particle moves in a circle describing equal angles in equal intervals of time, then its velocity vector

Slope of a position-time graph determines

Velocity of an insect crawling on a surface rectilinearly varies as v = 3t² – 2. The equation that holds good for analysing its motion is (symbols have usual meaning)

A lift starts moving up with an acceleration of 2 m/s². After one second a bolt drops from the ceiling. The time after which it will strike the floor of 1.2 m high lift is (Take g = 10 m/s²)

A vehicle covers one fourth of total distance with speed v₁ and remaining part with speed v₂ then its average speed is

The acceleration-time (a–t) graph of a particle moving along a straight line is as shown in figure. If initial velocity of particle is 5 m/s, then velocity at the end of 7 second is

A police jeep chasing a thief’s car which is moving at 40 m/s on a straight track. If separation between the jeep and car is 400 m, then minimum speed (assuming uniform) of jeep required to catch the car in 20 s is

A particle starts from rest and moves at an acceleration of 4 m/s² for 10 second and then decelerates uniformly for another 5 second to come to rest. Distance covered by particle in this journey is

A particle is moving along x-axis such that its position (x) varies with time (t) as x = t sin t. The average acceleration of the particle from t = 0 s to t = /2 s is

A stone dropped from the top of a tower is found to travel 7/16 of the height of tower during the last second of its fall. The total time of fall is

A ball is thrown at angle θ and another ball is thrown at an angle (90°–θ) with horizontal direction from the same point each with speed 30 m/s. The ratio of maximum height attained by them will be.

A particle starts from rest, moves with constant acceleration for 10 s. If it covers s₁ distance in first 5 s then distance s₂ in next 5 s, then the correct relation between s₁ and s₂ is

A particle moving on a straight line has initial velocity 2.03 m/s accelerating uniformly with 1.0 m/s² after 0.3 s will have a velocity (in m/s) of (upto correct significant figures)

Given below are two statements: Statement-I: The speed of a body moving in straight line can be negative. Statement-II: If a body is moving opposite to the direction of +x axis in straight line, its speed is negative. In the light of the above statem

An object is thrown vertically upward from ground with initial velocity 20 m/s. (Take g = 10 m/s²)

The position-time graph for two particles A and B are shown. The ratio of magnitude of their velocities (VA/VB) is;

For the velocity-time graph shown in figure, the distance covered by body in first 5 seconds is;

The position-time (s-t) graph of a particle is shown in figure. The magnitude of instantaneous velocity of particle is maximum at point;

A particle has acceleration (a) according to the graph shown. If velocity of particle at t = 0 is 5 m/s, then velocity of particle at t = 10 s is;

The time-velocity graph of a particle moving in straight line is shown in figure. Acceleration of particle at t = 2 s is;

For a particle moving in straight line, which of the following relation between velocity of particle v and time t represent uniform motion?

The relation t = √x + 3 describes the position of a particle, where x is in meters and t is in seconds. The position, when velocity is zero, is;

The velocity of a body depends on time according to the equation v = 10 + 0.1t². The body has;

Position of a particle varies with time as x = a cos t (where a is constant). Acceleration of particle at any time t is;

A particle moves along a straight line such that its position at any time (t) is given by s = (t³ − 6t² + 2) m. The velocity of the particle when the acceleration is zero, is;

The position of a particle is described by the equation y = pt² + qt + 1 (where p and q are positive constants). Velocity of particle at any time t is;

The acceleration of a particle related to time t as a = (2t − 1) m/s². The acceleration of particle will be zero at;

A particle is moving in a straight line. The velocity of the particle is given by equation v = (3t² + 5t) m/s. The velocity of particle at t = 2 s is;

Water drops fall at regular time interval from a tap 5 m above the ground. Time taken by first drop to reach the ground is (g = 10 m/s²)

If an iron ball and a wooden ball of same radius are released from rest from a height h in vacuum. The time taken by iron ball to reach ground will be;