Motion in a straight line practice · Mixed difficulty

A car travels along a straight line for the first half time with speed $50 \mathrm{~kmh}^{-1}$ and the second half time with speed $60 \mathrm{~kmh}^{-1}.$ Find the average speed of the car.

The driver of an express train moving with a velocity ${v_1}$ finds that a goods train is moving with a velocity ${v_2}$ in the same direction on the same track. He applies the brakes and produces a retardation a. The minimum time required to avoid collision is

If a body having initial velocity zero is moving with uniform acceleration $8 \mathrm{~m} / \mathrm{sec}^2$, the distance travelled by it in fifth second will be

The relation between acceleration and velocity for a body moving in straight line is $a \propto v^3$. Choose incorrect option. ($x$ is position and $t$ is time)

Assertion: If two particles, moving with constant velocities are to meet, the relative velocity must be along the line joining the two particles.
Reason: Relative velocity means motion of one particle as viewed by the other.

Two balls $A$ and $B$ are placed at the top of $180 \mathrm{~m}$ tall tower. Ball $A$ is released from the top at $t=0 \mathrm{~s}$. Ball $B$ is thrown vertically down with an initial velocity $u$ at $t=2 \mathrm{~s}$. After a certain time, both balls meet $100 \mathrm{~m}$ above the ground. Find the value of $u$ in $\mathrm{ms}^{-1}$ [use $g=10 \mathrm{~ms}^{-2}$ ]

A train $175 \mathrm{~m}$ long crosses a bridge which is $225 \mathrm{~m}$ long in 80 seconds. What is the speed of the train?

The motion of a particle moving along $y$-axis is represented as $y=3(t-2)+5(t-2)^2.$ Identify the correct statement.

A graph is drawn between velocity and time for the motion of a particle. The area under the curve between the time intervals ${t_1}\,and\,\,{t_2}$ gives

Assertion (A) : A body is dropped from height $h$ and another body is thrown vertically upwards with a speed $\sqrt{g h}$. They meet at height $h / 2$.

Reason (R) : The time taken by both the blocks in reaching the height $h / 2$ is same.

The displacement of a particle starting from rest (at t=0) is given by $s = 6{t^2} - {t^3}.$. The time in seconds at which the particle will attain zero velocity again, is

A body starts from rest and travels a distance S with uniform acceleration, then moves uniformly a distance 2 S uniformly, and finally comes to gest after moving further 5 S under uniform retardation. The ratio of average velocity to maximum velocity is

Two trains $121 \mathrm{~m}$ and $99 \mathrm{~m}$ in lengths are running in opposite directions with velocities $40 \mathrm{~km} / \mathrm{h}$ and $32 \mathrm{~km} / \mathrm{h}$. In what time they will completely cross each other?

The displacement of particle is given by $y = 2 + 3t + 8{t^2} - 6{t^4}\,\,{\text{m}}$ then initial velocity is given by (m/s)

A person travels along a straight road for the first half time with a velocity $v_1$ and the second half time with a velocity $v_2$. Then the mean velocity $\bar{v}$ is given by

A bus starts from rest and moves along a straight road with constant acceleration $f$ until its speed is $v$. The bus then continues with constant speed $v$. When the bus starts, a car is at a distance $b$ behind the bus and is moving with constant speed $u$ in same direction as that of bus. Find the distance between the car and the bus at time $t$ after the bus started.

(Given $0 < t < \frac{v}{f}$ and $u^2 < 2 f b$).

A body is moving with uniform velocity of $8 \mathrm{~ms}^{-1}$. When the body just crossed another body, the second one starts and moves with uniform acceleration of $4 \mathrm{~ms}^{-2}$. The time after which two bodies meet, will be

A train is moving with a velocity of $30 \mathrm{~ms}^{-1}$. When brakes are applied, it is found that the velocity reduced to $10 \mathrm{~ms}^{-1}$ in $240 \mathrm{~m}$. When the velocity of the train is zero, the distance travelled is

A train started from rest from a station and accelerated at $2\,m{s^{ - 2}}$ for 10sec. Then it travels at constant speed for 30 sec and there after it decelerated at $4\,m{s^{ - 2}}$ until it stopped at the next station. The distance between two stations is

A ball which is at rest is dropped from a height h metre. As it bounces off the floor its speed is 80% of what it was just before touching the ground. The ball then rise to nearly a height

Two stones of equal masses are dropped from a rooftop of height h one after another. Their separation distance against time will

Assertion(A): Average velocity can't be zero in case of uniform acceleration.

Reason (R): For average velocity to be zero, a non zero velocity should not remain constant.

Assertion: In one-dimensional motion of an object, path length comes out to be equal to displacement.
Reason: Direction of object is changed two times.

A body is thrown vertically upwards with a velocity u. Find the true statement from the following

The distance x covered by a particle in one-dimensional motion varies with time t as ${x^2} = a{t^2} + 2bt + c$. The accelerating of the particle varies as

Assertion: An object may have varying speed without having varying velocity.
Reason: If the velocity is zero at an instant, the acceleration may not be zero at that instant.

Assertion: For a moving object the instantaneous velocity is calculated by the limiting value of its average velocity as the time interval approaches to zero.
Reason: The direction of the average velocity is same as the direction of displacement.

Assertion: For an object in uniform motion, the position-time graph is a straight line inclined to the time-axis.

Reason: In a uniform motion, the acceleration is zero.

A particle starts from the origin of coordinates at time t=0 and moves in the x-y plane with a constant acceleration&nbsp;$\alpha$ in the y-diretion. Its equation of motion is $y = \mathrm{\beta }{x^2}$. Its velocity component in the x-direction is

A particle moves in a straight line, so that after $t$ second the distance $x$ from a fixed point $O$ on the line is given by $x=(t-2)^2(t-5)$. Then