Motion in a Straight Line

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JEE Main 2021

A particle is projected with velocity $v_{0}$ along X-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin, i.e. $ma = - α x^{2}$ . The distance at which the particle stops is

(\frac{3 m v _{0}^{2}}{2 α})^{1/2}

(B)

(\frac{2 m v _{0}^{3}}{3 α})^{1/3}

(C)

(\frac{2 m v _{0}^{2}}{3 α})^{1/2}

(D)

(\frac{3 m v _{0}^{2}}{2 α})^{1/3}

JEE Main 2020 (08 Jan Shift 2)

LEVELJEE Main

A ball is dropped from the top of a $100 m$ high tower on a planet. In the last $\frac{1}{2} s$ before hitting the ground, it covers a distance of $19 m$ . Acceleration due to gravity (in $ms^{- 2}$ ) near the surface on that planet is ........... .

JEE Main 2019, 12 April Shift-II

LEVELJEE Main

A particle is moving with speed $v = b x$ along positive X-axis. Calculate the speed of the particle at time $t = τ$ (assume that the particle is at origin at $t = 0$ ).

(A)

\frac{b ^{2} τ}{4}

(B)

\frac{b ^{2} τ}{2}

(C)

b^{2} τ

(D)

\frac{b ^{2} τ}{2}

JEE Main 2021, 26 Feb Shift-II

LEVELJEE Main

A scooter accelerates from rest for time $t_{1}$ at constant rate $a_{1}$ and then retards at constant rate $a_{2}$ for time $t_{2}$ and comes to rest. The correct value of $\frac{t _{1}}{t _{2}}$ will be

(A)

\frac{a _{1} + a _{2}}{a _{2}}

(B)

\frac{a _{2}}{a _{1}}

(C)

\frac{a _{1}}{a _{2}}

(D)

\frac{a _{1} + a _{2}}{a _{1}}

JEE Main 2021, 25 July Shift-II

LEVELJEE Main

The relation between time $t$ and distance $x$ for a moving body is given as $t = m x^{2} + n x$ , where $m$ and $n$ are constants. The retardation of the motion is (when $v$ stands for velocity)

(A)

2 m v^{3}

(B)

2 mn v^{3}

(C)

2 n v^{3}

(D)

2 n^{2} v^{3}

LEVELJEE Main

An object moving with a speed of $6.25 m/s$ , is decelerated at a rate given by $\frac{d v}{d t} = - 2.5 v$ , where $v$ is the instantaneous speed. The time taken by the object to come to rest, would be

(A)

2 s

(B)

4 s

(C)

8 s

(D)

1 s

LEVELJEE Main

A ball is released from the top of a tower of height $h$ metre. It takes $T$ second to reach the ground. What is the position of the ball in $T /3$ second?

(A)

h /9

m from the ground

(B)

7 h /9

m from the ground

(C)

8 h /9

m from the ground

(D)

17 h /18

m from the ground

JEE Main 2020, 4 Sep Shift-I

LEVELJEE Main

A tennis ball is released from a height $h$ and after freely falling on a wooden floor, it rebounds and reaches height $h /2$ . The velocity versus height of the ball during its motion may be represented graphically by (Graphs are drawn schematically and on not to scale)

JEE Main 2021, 27 July Shift-I

LEVELJEE Advanced

A ball is thrown up with a certain velocity, so that it reaches a height $h$ . Find the ratio of the two different times of the ball reaching $\frac{h}{3}$ in both the directions.

(A)

\frac{2 - 1}{2 + 1}

(B)

\frac{1}{3}

(C)

\frac{3 - 2}{3 + 2}

(D)

\frac{3 - 1}{3 + 1}

JEE Main 2020, 5 Sep Shift-I

LEVELJEE Advanced

A helicopter rises from rest on the ground vertically upwards with a constant acceleration $g$ . A food packet is dropped from the helicopter when it is at a height $h$ . The time taken by the packet to reach the ground is close to (Here, $g$ is the acceleration due to gravity).

(A)

t = \frac{2}{3} \frac{h}{g}

(B)

t = 1.8 \frac{h}{g}

(C)

t = \frac{2 h}{3 g}

(D)

t = 3.4 \frac{h}{g}

JEE Main 2019, 9 April Shift-II

LEVELJEE Main

The position of a particle as a function of time $t$ , is given by $x (t) = a t + b t^{2} - c t^{3}$ where $a, b$ and $c$ are constants. When the particle attains zero acceleration, then its velocity will be

(A)

a + \frac{b ^{2}}{2 c}

(B)

a + \frac{b ^{2}}{4 c}

(C)

a + \frac{b ^{2}}{3 c}

(D)

a + \frac{b ^{2}}{c}

JEE Main 2021, 25 July Shift-II

LEVELJEE Main

The instantaneous velocity of a particle moving in a straight line is given as $v = α t + β t^{2}$ , where $α$ and $β$ are constants. The distance travelled by the particle between $1 s$ and $2 s$ is

(A)

3 α + 7 β

(B)

\frac{3}{2} α + \frac{7}{3} β

(C)

\frac{α}{2} + \frac{β}{3}

(D)

\frac{3}{2} α + \frac{7}{2} β

JEE Main 2021, 27 Aug Shift-II

LEVELJEE Main

Water drops are falling from a nozzle of a shower onto the floor, from a height of $9.8 m$ . The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.

(A)

4.18 m

(B)

2.94 m

(C)

2.45 m

(D)

7.35 m

JEE Main 2021, 27 Aug Shift-I

LEVELBoard

If the velocity of a body related to displacement $x$ is given by $v = 5000 + 24 x$ m/s, then the acceleration of the body is ...... m/s $^{2}$ .

JEE Main 2021, 26 Aug Shift-I

LEVELJEE Main

Two spherical balls having equal masses with radius of $5 cm$ each are thrown upwards along the same vertical direction at an interval of $3 s$ with the same initial velocity of $35 m/s$ , then these balls collide at a height of .......... $m$ . (Take, $g = 10 m/s^{2}$ )

LEVELJEE Main

A particle located at $x = 0$ at time $t = 0$ , starts moving along the positive x-direction with a velocity $v$ that varies as $v = α x$ . The displacement of the particle varies with time as

(A)

t^{2}

(B)

t

(C)

t^{1/2}

(D)

t^{3}

JEE Main 2019, 9 Jan Shift-II

LEVELJEE Advanced

In a car race on a straight path, car A takes a time t less than car B at the finish and passes finishing point with a speed 'v' more than that of car B. Both the cars start from rest and travel with constant acceleration $a_{1}$ and $a_{2}$ respectively. Then 'v' is equal to

(A)

\frac{2 a _{1} a _{2}}{a _{1} + a _{2}} t

(B)

2 a_{1} a_{2} t

(C)

a_{1} a_{2} t

(D)

\frac{a _{1} + a _{2}}{2} t

JEE Main 2021, 17 March Shift-II

LEVELJEE Main

The velocity of a particle is $v = v_{0} + g t + F t^{2}$ . Its position is $x = 0$ at $t = 0$ , then its displacement after time ( $t = 1$ ) is

(A)

v_{0} + g + F

(B)

v_{0} + \frac{g}{2} + \frac{F}{3}

(C)

v_{0} + \frac{g}{2} + F

(D)

v_{0} + 2 g + 3 F

JEE Main 2020

LEVELJEE Advanced

The distance $x$ covered by a particle in one dimensional motion varies with time $t$ as $x^{2} = a t^{2} + 2 b t + c$ . If the acceleration of the particle depends on $x$ as $x^{- n}$ , where $n$ is an integer, the value of $n$ is ...... .

JEE Main 2021, 25 July Shift-I

LEVELJEE Main

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th second after its fall to the next droplet is $34.3 m$ . At what rate, the droplets are coming from the tap ? (Take, $g = 9.8 m/s^{2}$ )

A parachutist after bailing out falls $50 m$ without friction. When parachute opens, it decelerates at $2 ms^{- 2}$ . He reaches the ground with a speed of $3 ms^{- 1}$ . At what height, did he bail out?

(A)

91 m

(B)

182 m

(C)

293 m

(D)

111 m

JEE Main 2021, 25 July Shift-II

LEVELJEE Main

A balloon was moving upwards with a uniform velocity of $10 m/s$ . An object of finite mass is dropped from the balloon when it was at a height of $75 m$ from the ground level. The height of the balloon from the ground when object strikes the ground was around, is (Take, the value of $g = 10 m/s^{2}$ )

From a tower of height $H$ , a particle is thrown vertically upwards with a speed $u$ . The time taken by the particle to hit the ground is $n$ times that taken by it to reach the highest point of its path. The relation between $H$ , $u$ and $n$ is

(A)

2 g H = n^{2} u^{2}

(B)

g H = (n - 2)^{2} u^{2}

(C)

2 g H = n u^{2} (n - 2)

(D)

g H = (n - 2)^{2} u^{2}

LEVELJEE Main

The velocity of a particle is $v = v_{0} + g t + f t^{2}$ . If its position is $x = 0$ at $t = 0$ , then its displacement after unit time ( $t = 1$ ) is

(A)

v_{0} + 2 g + 3 f

(B)

v_{0} + \frac{g}{2} + \frac{f}{3}

(C)

v_{0} + g + f

(D)

v_{0} + \frac{g}{2} + f

JEE Main 2020, 5 Sep Shift-I

LEVELJEE Main

A balloon is moving up in air vertically above a point A on the ground. When it is at a height $h_{1}$ , a girl standing at a distance $d$ (point B) from A (see figure) sees it at an angle $4 5^{\circ}$ with respect to the vertical. When the balloon climbs up a further height $h_{2}$ , it is seen at an angle $6 0^{\circ}$ with respect to the vertical if the girl moves further by a distance $2.464 d$ (point C). Then, the height $h_{2}$ is (Given, $tan 3 0^{\circ} = 0.5774$ )

(A)

1.464 d

(B)

d

(C)

0.464 d

(D)

0.732 d

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A particle is moving with speed v=bx​ along positive X-axis. Calculate the speed of the particle at time t=τ (assume that the particle is at origin at t=0).

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The relation between time t and distance x for a moving body is given as t=mx2+nx, where m and n are constants. The retardation of the motion is (when v stands for velocity)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A ball is released from the top of a tower of height h metre. It takes T second to reach the ground. What is the position of the ball in T/3 second?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A ball is thrown up with a certain velocity, so that it reaches a height h. Find the ratio of the two different times of the ball reaching 3h​ in both the directions.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the velocity of a body related to displacement x is given by v=5000+24x​ m/s, then the acceleration of the body is ...... m/s2.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The velocity of a particle is v=v0​+gt+Ft2. Its position is x=0 at t=0, then its displacement after time (t=1) is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The velocity of a particle is v=v0​+gt+ft2. If its position is x=0 at t=0, then its displacement after unit time (t=1) is

A particle is moving with speed $v = b x$ along positive X-axis. Calculate the speed of the particle at time $t = τ$ (assume that the particle is at origin at $t = 0$ ).

The relation between time $t$ and distance $x$ for a moving body is given as $t = m x^{2} + n x$ , where $m$ and $n$ are constants. The retardation of the motion is (when $v$ stands for velocity)

A ball is released from the top of a tower of height $h$ metre. It takes $T$ second to reach the ground. What is the position of the ball in $T /3$ second?

A ball is thrown up with a certain velocity, so that it reaches a height $h$ . Find the ratio of the two different times of the ball reaching $\frac{h}{3}$ in both the directions.

If the velocity of a body related to displacement $x$ is given by $v = 5000 + 24 x$ m/s, then the acceleration of the body is ...... m/s $^{2}$ .

The velocity of a particle is $v = v_{0} + g t + F t^{2}$ . Its position is $x = 0$ at $t = 0$ , then its displacement after time ( $t = 1$ ) is

The velocity of a particle is $v = v_{0} + g t + f t^{2}$ . If its position is $x = 0$ at $t = 0$ , then its displacement after unit time ( $t = 1$ ) is