Motion Graphs

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JEE Main 2019, 9 April Shift-I

LEVELJEE Main

A ball is thrown vertically up (taken as + Z-axis) from the ground. The correct momentum-height (p-h) diagram is

JEE Main 2021, 17 March Shift-I

LEVELJEE Main

A car accelerates from rest at a constant rate $α$ for some time after which it decelerates at a constant rate $β$ to come to rest. If the total time elapsed is $t$ seconds, the total distance travelled is

(A)

\frac{4 α β}{( α + β )} t^{2}

(B)

\frac{2 α β}{( α + β )} t^{2}

(C)

\frac{α β}{2 ( α + β )} t^{2}

(D)

\frac{α β}{4 ( α + β )} t^{2}

JEE Main 2020, 4 Sep Shift-II

LEVELBoard

The speed versus time graph for a particle is shown in the figure. The distance travelled (in metre) by the particle during the time interval $t = 0 s$ to $t = 5 s$ will be ……… .

JEE Main 2018

LEVELJEE Main

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

(A)

Velocity vs Position Graph

(B)

Distance vs Time Graph

(C)

Position vs Time Graph

(D)

Velocity vs Time Graph

JEE Main 2021, 16 March Shift-I

LEVELJEE Advanced

The velocity-displacement graph describing the motion of a bicycle is shown in the following figure. The acceleration-displacement graph of the bicycle's motion is best described by

A body is at rest at $x = 0$ . At $t = 0$ , it starts moving in the positive x-direction with a constant acceleration. At the same instant, another body passes through $x = 0$ moving in the positive x-direction with a constant speed. The position of the first body is given by $x_{1} (t)$ after time $t$ and that of the second body by $x_{2} (t)$ after the same time interval. Which of the following graphs correctly describes $(x_{1} - x_{2})$ as a function of time?

JEE Main 2021, 18 March Shift-I

LEVELJEE Main

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by

JEE Main 2021, 31 Aug Shift-II

LEVELJEE Main

A particle is moving with constant acceleration $a$ . Following graph shows $v^{2}$ versus $x$ (displacement) plot. The acceleration of the particle is ........ $m/s^{2}$

JEE Main 2019, 8 April Shift-II

LEVELJEE Main

A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive X-axis. Identify all figures that correctly represent the motion qualitatively. ( $a = acceleration$ , $v = velocity$ , $x = displacement$ , $t = time$ )

JEE Main 2019, 10 Jan Shift-II

LEVELJEE Main

A particle starts from the origin at time $t = 0$ and moves along the positive X-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time $t = 5 s$ ?

JEE Main 2021, 18 March Shift-II

LEVELJEE Advanced

The velocity- displacement graph of a particle is shown in the figure. The acceleration-displacement graph of the same particle is represented by

JEE Main 2020, 5 Sep Shift-II

LEVELJEE Main

The v-t graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 s. The total distance covered by the body in 6 s is

(A)

\frac{37}{3}

\frac{49}{4}

LEVELJEE Main

Consider a rubber ball freely falling from a height $h = 4.9 m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then, the velocity as a function of time the height as function of time will be

A car starting from rest, accelerates at the rate $f$ through a distance $s$ , then continues at constant speed for time $t$ and then decelerates at the rate $f /2$ to come to rest. If the total distance travelled is $15 s$ , then

(A)

s = f t

(B)

s = \frac{1}{6} f t^{2}

(C)

s = \frac{1}{2} f t^{2}

A particle starts from rest. Its acceleration ( $a$ ) versus time ( $t$ ) is as shown in the figure. The maximum speed of the particle will be

(A)

110 m/s

(B)

55 m/s

(C)

550 m/s

(D)

660 m/s

JEE Advanced 2005

LEVELJEE Main

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement? (2005)

A particle of mass $m$ moves on the $x$ -axis as follows : it starts from rest at $t = 0$ from the point $x = 0$ and comes to rest at $t = 1$ at the point $x = 1$ . No other information is available about its motion at intermediate times ( $0 < t < 1$ ). If $α$ denotes the instantaneous acceleration of the particle, then

* Multiple Correct Options

(A)

α

cannot remain positive for all

t

in the interval

0 \leq t \leq 1

(B)

∣ α ∣

cannot exceed 2 at any point in its path

(C)

∣ α ∣

must be

\geq 4

at some point or points in its path

(D)

α

must change sign during the motion, but no other assertion can be made with the information given

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

Relation between average velocity $v_{a v}$ of a body and time $t$ is shown in the graph. If during the time interval considered, the body did not change direction of motion, draw a graph between instantaneous velocity of the body and time.

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

To study effect of air resistance, a rubber ball was shot vertically upwards from a spring gun from $2 0^{th}$ floor of a tall building. Velocity of the ball was recorded at regular intervals of time and the data obtained were plotted on a graph paper. Some of the marking on the axes are erased as shown in the following figure. With what speed did the ball strike the ground?

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

Two particles A and B start from the same point and move in the positive $x$ -direction. In a time interval of $2.00 s$ after they start, their velocities $v$ vary with time $t$ as shown in the following figures. What is the maximum separation between the particles during this time interval?

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

A material particle is chasing another one and both of them are moving on the same straight line. After they pass a particular point, their velocities $v$ vary with time $t$ as shown in the figure. When will the chase end?

Insufficient information.

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

Comprehension Passage

There is a narrow bridge somewhere on a road connecting two towns. Two cars travel from one of the towns to the other with a constant speed

v_{1}

everywhere on the road, except on the bridge, where they travel with another constant speed

v_{2}

. How the separation

s

between the cars varies with time

t

is shown in the following graph.

Question 1:

Two cars A and B simultaneously start a race. Velocity $v$ of the car A varies with time $t$ according to the graph shown in the figure. It acquires a velocity $50 m/s$ few seconds before $t = 100 s$ and thereafter moves with this speed. Car B runs together with car A till both acquire a velocity $20 m/s$ , after this car B moves with zero acceleration for one second and then follows velocity-time profile identical to that of A with a delay of one second. In this way, car B acquires the velocity $50 m/s$ one second after A acquires it. How much more distance $Δ s$ does the car A cover in the first $100 s$ as compared to the car B?

(A)

Δ s = 30 m

(B)

Δ s < 30 m

(C)

Δ s = 20 m

(D)

Insufficient information.

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

A ball is thrown vertically upwards. Its distance $s$ from a fixed point varies with time $t$ according to the following graph. Calculate velocity of projection of the ball.

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

Comprehension Passage

A stone is dropped from the top of a tower and before it hits the ground another stone is also dropped. Separation

s

between the stones is plotted against time

t

assuming that the stones do not bounce from the ground. Portions OA and BC of the graph are parabolic, while portion AB is a straight line. Acceleration due to gravity is

10 m/s^{2}

Question 1:

Height of the tower is

When the first stone hits the ground, the second stone was moving with

(A)

10 m/s at a height 40 m.

(B)

10 m/s at a height 25 m.

(C)

20 m/s at a height 20 m.

(D)

20 m/s at a height 25 m.

A ball is thrown vertically up (taken as + Z-axis) from the ground. The correct momentum-height (p-h) diagram is

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

The velocity-displacement graph describing the motion of a bicycle is shown in the following figure. The acceleration-displacement graph of the bicycle's motion is best described by

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A particle is moving with constant acceleration a. Following graph shows v2 versus x (displacement) plot. The acceleration of the particle is ........ m/s2

The velocity- displacement graph of a particle is shown in the figure. The acceleration-displacement graph of the same particle is represented by

The v-t graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 s. The total distance covered by the body in 6 s is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement? (2005)

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } What is the speed v1​ of the cars on the road?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } What is the speed v2​ of the cars on the bridge?

What is length of the bridge?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A ball is thrown vertically upwards. Its distance s from a fixed point varies with time t according to the following graph. Calculate velocity of projection of the ball.

Comprehension Passage

Height of the tower is

When the first stone hits the ground, the second stone was moving with

A particle is moving with constant acceleration $a$ . Following graph shows $v^{2}$ versus $x$ (displacement) plot. The acceleration of the particle is ........ $m/s^{2}$

A particle starts from rest. Its acceleration ( $a$ ) versus time ( $t$ ) is as shown in the figure. The maximum speed of the particle will be

What is the speed $v_{1}$ of the cars on the road?

What is the speed $v_{2}$ of the cars on the bridge?

A ball is thrown vertically upwards. Its distance $s$ from a fixed point varies with time $t$ according to the following graph. Calculate velocity of projection of the ball.