Chapter: Motion in a Straight Line

A person travelling in a straight line moves with a constant velocity \(\begin{align}{{v}_{1}}\end{align}\) for certain distance \(\begin{align}'x'\end{align}\) and with a constant velocity \(\begin{align}{{v}_{2}}\end{align}\) for next equal distance. The average velocity \(\begin{align}v\end{align}\) is given by the relation

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time \(\begin{align}{{t}_{1}}\end{align}\) . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time \(\begin{align}{{t}_{2}}\end{align}\) . The time taken by her to walk up on the moving escalator will be

If the velocity of a particle is \(\begin{align}v=At+b{{t}^{2}}\end{align}\),where A and B are constants, then the distance travelled by it between \(\begin{align}1s\end{align}\)and \(\begin{align}2s\end{align}\) is

Two cars \(\begin{align}P\end{align}\) and \(\begin{align}Q\end{align}\) start from a point at the same time in a straight line and their positions are represented by \(\begin{align}{{X}_{P}}(T)=at+b{{t}^{2}}\end{align}\)and \(\begin{align}{{X}_{0}}(t)=ft-{{t}^{2}}\end{align}\). At what time do the cars have the same velocity?

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to \(\begin{align}v(x)=\beta {{x}^{{-2n}}}\end{align}\) where, \(\begin{align}\beta \end{align}\) and n are constants and x is the position of the particle. The acceleration of the particle as a function of \(\begin{align}x\end{align}\), is given by

The motion of a particle along a straight line is described by equation \(\begin{align}x=8+12t-{{t}^{3}}\end{align}\)where, \(\begin{align}x\end{align}\) is in metre and \(\begin{align}t\end{align}\) in sec. The retardation of the particle when its velocity becomes zero, is

A body is moving with velocity \(\begin{align}30m/s\end{align}\)towards East. After 10s, its velocity becomes \(\begin{align}40m/s\end{align}\)towards North. The average acceleration of the body is

A particle moves a distance \(\begin{align}x\end{align}\) in time \(\begin{align}t\end{align}\) according to the equation \(\begin{align}x={{(t+5)}^{{-1}}}\end{align}\). The acceleration of particle is proportional to

A bus is moving with a speed of \(\begin{align}10m{{s}^{{-1}}}\end{align}\)on a straight road. A scooterist wishes to overtake the bus in \(\begin{align}100s\end{align}\). If the bus is at a distance of \(\begin{align}1km\end{align}\)from the scooterist, with what speed should the scooterist chase the bus?

A particle moving along x-axis has acceleration \(\begin{align}f\end{align}\), at time \(\begin{align}t\end{align}\), given by \(\begin{align}f=\text{ }{{f}_{0}}\text{ }\left( {1-\frac{t}{T}} \right)\end{align}\), where \(\begin{align}{{f}_{0}}\end{align}\) and \(\begin{align}\text{T}\end{align}\) are constants. The particle at \(\begin{align}\text{t=0}\end{align}\) has zero velocity. In the time interval between \(\begin{align}\text{t=0}\end{align}\)and the instant when \(\begin{align}\text{f=0}\end{align}\),the particle’s velocity \(\begin{align}\left( {{{v}_{x}}} \right)\end{align}\)is

A car moves from \(\begin{align}X\end{align}\) to\(\begin{align}Y\end{align}\)with a uniform speed\(\begin{align}{{v}_{u}}\end{align}\) and returns to \(\begin{align}X\end{align}\) with a uniform speed \(\begin{align}{{v}_{d}}\end{align}\) . The average speed for this round trip is

The position x of a particle w.r.t. time \(\begin{align}t\end{align}\) along \(\begin{align}x-axis\end{align}\)is given by \(\begin{align}x=9{{t}^{2}}-{{t}^{3}}\end{align}\),where \(\begin{align}x\end{align}\) is in metre and \(\begin{align}t\end{align}\) in sec. What will be the position of this particle when it achieves maximum speed along the \(\begin{align}+x\end{align}\)direction?

A particle moves along a straight line \(\begin{align}OX\end{align}\). At a time \(\begin{align}t\end{align}\) (in second), the distance \(\begin{align}x\end{align}\) (in metre) of the particle from \(\begin{align}O\end{align}\) is given by \(\begin{align}x=40+12t-{{t}^{3}}\end{align}\)– How long would the particle travel before coming to rest?

The displacement \(\begin{align}\text{x}\end{align}\) of a particle varies with time \(\begin{align}t\end{align}\) as \(\begin{align}\text{x=a}{{\text{e}}^{{-\alpha t}}}\text{+b}{{\text{e}}^{{\beta t}}}\end{align}\), wherea \(\begin{align}\text{a,b,}\alpha \end{align}\) and \(\begin{align}\beta \end{align}\) are positive constants. The velocity of the particle will

A particle moves along a straight line such that its displacement at any time t is given by \(\begin{align}s=3{{t}^{3}}+7{{t}^{2}}+14t+5\end{align}\) .The acceleration of the particle at \(\begin{align}t=1s\end{align}\)is

The position \(\begin{align}x\end{align}\) of a particle varies with time \(\begin{align}t\end{align}\),as \(\begin{align}x=a{{t}^{2}}-b{{t}^{3}}\end{align}\) . The acceleration of the particle will be zero at time \(\begin{align}t\end{align}\) equals to

A car accelerates from rest at a constant rate \(\begin{align}\alpha \end{align}\) for some time, after which it decelerates at a constant rate \(\begin{align}\beta \end{align}\) and comes to rest. If the total time elapsed is \(\begin{align}\text{t}\end{align}\), then the maximum velocity acquired by the car is

A particle moves along a straight line such that its displacement at any time \(\begin{align}t\end{align}\) is given by \(\begin{align}s=\left( {{{t}^{3}}-6{{t}^{2}}+3t+4} \right)m\end{align}\) The velocity when the acceleration is zero, is

A train of \(\begin{align}150m\end{align}\) length is going towards North direction at a speed of \(\begin{align}10m/s\end{align}\). A parrot flies at the speed of \(\begin{align}5m/s\end{align}\) towards South direction parallel to the railways track. The time taken by the parrot to cross the train is

A bus travelling the first one-third distance at a speed of \(\begin{align}10km/h\end{align}\), the next one-third at \(\begin{align}20km/h\end{align}\)and the last one-third at \(\begin{align}60km/h\end{align}\). The average speed of the bus is

A car moves a distance of \(\begin{align}200m\end{align}\). It covers the first-half of the distance at speed \(\begin{align}40km/h\end{align}\) and the second-half of distance at speed \(\begin{align}vkm/h\end{align}\). The average speed is \(\begin{align}48km/h\end{align}\). Find the value of \(\begin{align}v\end{align}\).

A car covers the first-half of the distance between two places at \(\begin{align}40km/h\end{align}\) and other half at \(\begin{align}60km/h\end{align}\). The average speed of the car is

A car starts from rest and accelerates at \(\begin{align}5m/{{s}^{2}}\end{align}\). At \(\begin{align}t=4s\end{align}\), a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at \(\begin{align}t=6s\end{align}\)? (Take,\(\begin{align}g=10m/{{s}^{2}}\end{align}\))

A small block slides down on a smooth inclined plane, starting from rest at time \(\begin{align}\text{t=0}\end{align}\). Let \(\begin{align}{{\text{s}}_{n}}\end{align}\) be the distance travelled by the block in the interval \(\begin{align}\text{t=n-1}\end{align}\) to \(\begin{align}\text{t=n}\end{align}\) . Then, the ratio \(\begin{align}\frac{{{{s}_{n}}}}{{{{s}_{{n+1}}}}}\end{align}\) is

A person sitting in the ground floor of a building notices through the window of height \(\begin{align}1.5m\end{align}\), a ball dropped from the roof of the building crosses the window in \(\begin{align}0.1s\end{align}\). What is the velocity of the ball when it is at the topmost point of the window? \(\begin{align}(g=10m/{{s}^{2}})\end{align}\)

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is (g =10m/s₂ )

A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time t ₁ if the elevator is at rest and in time t ₂ if the elevator is moving uniformly. The which of the following option is correct?

A toy car with charge \(\begin{align}q\end{align}\) moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\begin{align}E\end{align}\). Due to the force\(\begin{align}qE\end{align}\), its velocity increases from \(\begin{align}0\end{align}\) to \(\begin{align}6m/s\end{align}\) in one second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between \(\begin{align}0\end{align}\) to \(\begin{align}3\end{align}\) seconds are respectively

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

A boy standing at the top of a tower of \(\begin{align}20m\end{align}\) height drops a stone. Assuming, \(\begin{align}g=10m{{s}^{{-2}}}\end{align}\), the velocity with which it hits the ground is

A ball is dropped from a high rise platform at \(\begin{align}t=0\end{align}\)starting from rest. After \(\begin{align}6s\end{align}\), another ball is thrown downwards from the same platform with a speed \(\begin{align}v\end{align}\) . The two balls meet at \(\begin{align}t=18s\end{align}\). What is the value of \(\begin{align}v\end{align}\)? \(\begin{align}(Takeg=10m{{s}^{{-2}}})\end{align}\)

A particle starts its motion from rest under the action of a constant force. If the distance covered in first \(\begin{align}10s\end{align}\) is \(\begin{align}{{s}_{1}}\end{align}\) and that covered in the first \(\begin{align}20s\end{align}\) is \(\begin{align}{{s}_{2}}\end{align}\) , then

A particle moves in a straight line with a constant acceleration. It changes its velocity from \(\begin{align}10m{{s}^{{-1}}}\end{align}\) − to \(\begin{align}20m{{s}^{{-1}}}\end{align}\) while passing through a distance \(\begin{align}135m\end{align}\) in \(\begin{align}t\end{align}\) sec. The value of \(\begin{align}t\end{align}\)is

The distance travelled by a particle starting from rest and moving with an acceleration \(\begin{align}\frac{4}{3}m{{s}^{{-2}}}\end{align}\) ,in the third-second is

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

A man throws balls with the same speed vertically upwards one after the other at an interval of \(\begin{align}\text{2s}\end{align}\). What should be the speed of the throw so that more than two balls are in the sky at any time? \(\begin{align}\text{(Takeg=9}\text{.8m/}{{\text{s}}^{2}}\text{) }\end{align}\)

If a ball is thrown vertically upwards with speed \(\begin{align}u\end{align}\), the distance covered during the last \(\begin{align}t\end{align}\) sec of its ascent is

A stone is thrown vertically upwards. When stone is at a height half of its maximum height, its speed is \(\begin{align}10m/s\end{align}\), then the maximum height attained by the stone is \(\begin{align}\left( {g=10m/{{s}^{2}}} \right)\end{align}\)

A car moving with a speed of \(\begin{align}40km/h\end{align}\)can be stopped after \(\begin{align}2m\end{align}\) by applying brakes. If the same car is moving with a speed of \(\begin{align}80km/h\end{align}\), what is the minimum stopping distance?

If a car at rest, accelerates uniformly to a speed of \(\begin{align}144km/h\end{align}\) in \(\begin{align}20s\end{align}\), it covers a distance of

If a ball is thrown vertically upwards with a velocity of \(\begin{align}\text{40m/s}\end{align}\), then velocity of the ball after \(\begin{align}\text{2s}\end{align}\) will be \(\begin{align}\left( {g=10m/{{s}^{2}}} \right)\end{align}\)

Three different objects of masses \(\begin{align}{{m}_{1}},{{m}_{2}}\end{align}\)and \(\begin{align}{{m}_{3}}\end{align}\) are allowed to fall from rest and from the same point \(\begin{align}0\end{align}\)along three different frictionless paths. The speeds of the three objects on reaching the ground will be in the ratio of

The water drops fall at regular intervals from a tap \(\begin{align}5m\end{align}\) above the ground. The third drop is leaving the tap at an instant when the first drop touches the ground. How far above the ground is the second drop at that instant ? \(\begin{align}\left( {Takeg=10m/{{s}^{2}}} \right)\end{align}\)

A body is thrown vertically upwards from the ground. It reaches a maximum height of \(\begin{align}\text{20m}\end{align}\) in \(\begin{align}\text{5s}\end{align}\). After what time it will reach the ground from its maximum height position ?

A stone released with zero velocity from the top of a tower, reaches the ground in \(\begin{align}\text{4s}\end{align}\). The height of the tower is \(\begin{align}\left( {g=10m/{{s}^{2}}} \right)\end{align}\)

A body starts from rest, what is the ratio of the distance travelled by the body during the 4th and 3rd\(\begin{align}\text{s}\end{align}\)?

A body dropped from top of a tower fall through \(\begin{align}40m\end{align}\) during the last two seconds of its fall. The height of tower is \(\begin{align}\left( {g=10m/{{s}^{2}}} \right)\end{align}\)

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

A car is moving along a straight road with a uniform acceleration. It passes through two points \(\begin{align}P\end{align}\) and \(\begin{align}Q\end{align}\) separated by a distance with velocity \(\begin{align}30km/h\end{align}\) and \(\begin{align}40km/h\end{align}\) respectively. The velocity of the car midway between \(\begin{align}P\end{align}\) and \(\begin{align}Q\end{align}\) is

A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point IMAGE 1

The displacement-time graph of moving particle is shown below. The instantaneous velocity of the particle is negative at the point IMAGE 2

Which of the following curves does not represent motion in one dimension?