The position (x)-time (t) graph for a particle moving along a straight line is shown in the figure. The average speed of particle in time interval t=0 to t=8 s is

A boat covers certain distance between two spots in a river taking t₁ hrs going downstream and t₂ hrs going upstream. What time will be taken by boat to cover same distance in still water?

A train of 150 m length is going towards North a speed of 10 m/s. A bird is flying at 5 m/s parallel to the track towards the South. The time taken by the to the track bird to cross the train is

Two cars are moving in the same direction with a speed of 30 km/h. They are separated from each other by 5 km. The third car moving in the opposite direction meets the two cars after an interval of 4 minutes. The speed of the third car is

Two cars A and B are moving in the same direction with velocities 30 m/s and 20 m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of 2 m/s². There will be no collision when

A ball is dropped from the top of a building of height 80 m. At the same instant, another ball is thrown upwards with a speed 50 m/s from the bottom of the building. The time at which balls will meet is-

An unloaded bus can be stopped by applying brakes on straight road after covering a distance x. Suppose, the passenger add 50% of its weight as the load and the braking force remains unchanged, how far will the bus go after the application of the brakes? (Velocity of bus in both case is same)

Figure below shows the velocity-time graph. This graph tells us that the body is:

In the following velocity-time graph of a body, the distance and displacement traveled by the body in 5 seconds in metres will be, respectively:

A body is thrown upwards and reaches its maximum height. At that position:

Among the four graphs shown in the figure, there is only one graph for which average velocity over the time interval (0, T) can vanish for a suitably chosen T. Select the graph.

A lift is coming from the 8th floor and is just about to reach the 4th floor. Taking ground floor as the origin and positive direction upwards for all quantities, which one of the following is correct:

If in one-dimensional motion, instantaneous speed v satisfies $0\le \mathrm{v}<{\mathrm{v}}_0$, then

A vehicle travels half the distance L with speed v₁ and the other half with speed v₂, then its average speed is

The displacement of a particle is given by x = ${(\mathrm{t} - 2)}^2$ where x is in meter and t in second. The. distance covered by the particle in the first 4 seconds is

At a metro station, a girl walks up a stationary escalator in time ${\mathrm{t}}_1$. If she remains stationary on the escalator, then the escalator takes her up in time ${\mathrm{t}}_2$. The time taken by her to walk upon the moving escalator will be:

The variation of quantity A with quantity B is plotted in the given figure which describes the motion of a particle in a straight line.
           
Consider the following statements:
a. Quantity B may represent time.
b. Quantity A is velocity if motion is uniform.
c. Quantity A is displacement if motion is uniform.
d. Quantity A is velocity if motion is uniformly accelerated.
Select the correct option:

Q.8 A graph of x versus t is shown in the figure. Choose correct alternatives given below.

(a) The particle was released from rest at = 0
(b) At B, the acceleration a > 0
(c) Average velocity for the motion between A and D is positive
(d) The speed at D exceeds that at E

Q.9 For the one-dimensional motion, described by x = t - sin t

(a) x(t) > 0 for all t > 0
(b) v(t) > 0 for all t > 0
(c) a(t) > 0 for all t > 0
(d) v(t) lies between 0 and 2

A ball is bouncing elastically with a speed of 1 m/s between walls of a railway compartment of size 10 m in a direction perpendicular to walls. The train is moving at a constant velocity of 10 m/s parallel to the direction of motion of the ball. As seen from the ground.
a. The direction of motion of the ball changes every 10 sec.
b. Speed of ball changes every 10 sec
c. Average speed of ball over any 20 sec intervals is fixed
d. The acceleration of the ball is the same as from the train

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

Refer to the graph in the figure. Match the following.

Graph         Characteristics

         (i) has v > 0 and a < 0 throughout

         (ii) has x > 0 throughout and has a point with v = 0 and a point with a = 0

         (iii) has a point with zero displacement for t > 0

         (iv) has v < 0 and a > 0

$$\begin{gathered} \left(1\right) \left(\mathrm{a}\right)-\left(\mathrm{ii}\right), \left(\mathrm{b}\right)-\left(\mathrm{iii}\right), \left(\mathrm{c}\right)-\left(\mathrm{i}\right), \left(\mathrm{d}\right)-\left(\mathrm{iv}\right) \\ \left(2\right) \left(\mathrm{a}\right)-\left(\mathrm{iv}\right), \left(\mathrm{b}\right)-\left(\mathrm{ii}\right), \left(\mathrm{c}\right)-\left(\mathrm{iii}\right), \left(\mathrm{d}\right)-\left(\mathrm{i}\right) \\ \left(3\right) \left(\mathrm{a}\right)-\left(\mathrm{iii}\right), \left(\mathrm{b}\right)-\left(\mathrm{ii}\right), \left(\mathrm{c}\right)-\left(\mathrm{iv}\right), \left(\mathrm{d}\right)-\left(\mathrm{i}\right) \\ \left(4\right) \left(\mathrm{a}\right)-\left(\mathrm{i}\right), \left(\mathrm{b}\right)-\left(\mathrm{ii}\right), \left(\mathrm{c}\right)-\left(\mathrm{iii}\right), \left(\mathrm{d}\right)-\left(\mathrm{iv}\right) \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. The variation of its acceleration with time is:

(Take acceleration in the backward direction as positive)

This objective question is based on NCERT Exemplar subjective Question.

The motion of a particle is represented by $\mathrm{x}\left(\mathrm{t}\right)=\mathrm{t}-\mathrm{sint}$. Then,

This objective question is based on NCERT Exemplar subjective Question.

The position of an object is given by $\mathrm{x}\left(\mathrm{t}\right) = \mathrm{A}+{\mathrm{Be}}^{-\mathrm{\gamma t}}, \mathrm{where} \mathrm{A}>\mathrm{B} \mathrm{and} \mathrm{\gamma }>0$, then at any time t:

This objective question is based on NCERT Exemplar subjective Question.

An object falling through a fluid is observed to have acceleration given by a = g - bv, where g = gravitational acceleration and b, is constant. After a long time of release, it is observed to fall with constant speed. The value of constant speed is:

$$\begin{gathered} \left(1\right) \frac{\mathrm{g}}{\mathrm{b}} \\ \left(2\right) \frac{\mathrm{g}}{{\mathrm{b}}^2} \\ \left(3\right) \frac{{\mathrm{g}}^2}{\mathrm{b}} \\ \left(4\right) \sqrt{\frac{\mathrm{g}}{\mathrm{b}}} \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

A ball is dropped and its displacement versus time graph is as shown. (Displacement x from the ground and all quantities are positive upwards).

The velocity-time graph of the ball is given by:

This objective question is based on NCERT Exemplar subjective question.

A car is moving along a straight line, say OP in the figure. It moves from O to P in 18 s and returns from P to Q in 6.0 s. The average velocity and average speed of the car in going from O to P and back to Q respectively are:

The position of an object moving along x-axis is given by x = $\mathrm{a}+{\mathrm{bt}}^2$ where a = 8.5 m, b = 2.5 ${\mathrm{ms}}^{-2}$ and t is measured in seconds. Its average velocity between t = 2.0 s and t = 4.0 s is:

Which of the following does not represent the equation of motion for constant acceleration?