Motion in a straight line practice · Mixed difficulty

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is ${S_1}$ and that covered in the first 20 seconds is ${S_2}$ , then

A body throws a ball in air in such a manner that when the ball is at its maximum heights he throws another ball. If the balls are thrown with the time difference 1 second, the maximum height attained by each ball is

Free fall of an object (in vacuum) is a case of motion with

A train is moving towards north. At one place, it turns towards north-east. Here, we observe that

The acceleration of a moving body can be found from

The initial velocity of a particle is $u$ and acceleration is given by at. Which of the following relations for the final velocity $\mathrm{v}$ is valid?

A ball is thrown horizontally from a height of $100 \mathrm{~m}$ with an initial speed of $15 \mathrm{~m} \mathrm{~s}^{-1}$. How far does it travel horizontally in the first 2 seconds?

Assertion : The speedometer of an automobile measure the average speed of the automobile.

Reason : Average velocity is equal to total displacement per total time taken.

An automobile travels on a straight road for $40 \mathrm{~km}$ at $30 \mathrm{~km}$ $\mathrm{h}^{-1}$. It then continues in the same direction for another $40 \mathrm{km}$ at $60 \mathrm{~km} \mathrm{~h}^{-1}$. What is the average velocity of the car during its $80 \mathrm{~km}$ trip?

Assertion: When the initial velocity is zero; then the final velocity value depends upon the acceleration and time taken by the particle

Reason: The kinematical equation of motion relating initial velocity, final velocity, acceleration and time taken by the particle is $v=u+a t$

A ball of mass ${m_1}$ and another ball of mass ${m_2}$ are dropped from equal height. If time taken by the balls are ${t_1}$ and ${t_2}$ respectively, then

A train accelerates from rest at a constant rate α for distance ${x_1}$ and time ${t_1}$. After that it retards to rest at constant rate $\beta$ for distance ${x_2}$ and time ${t_2}$. Then it is found that

Amongst the following equation of motion, which represents uniformly accelerated motion?

A particle is moving such that $s=t^3-6 t^2+18 t+9$, where $s$ is in metre and $t$ is in second. The minimum velocity attained by the particle is

A rocket is fired upward from the earth’s surface such that it creates an acceleration of $19.6\;m/{\sec ^2}.$⁡. If after 5 sec⁡ its engine is switched off, the maximum height of the rocket from earth’s surface would be

The ratio of the numerical values of the average velocity and average speed of a body is always

Two cars A and B are moving with same speed of 45 km/hr along same direction. If a third car C coming from the opposite direction with a speed of 36 km/hr meets two cars in an interval of 5 minutes, the distance of separation of two cars A and B should be (in km)

A body covers 26, 28, 30, 32 meters in 10th, 11th, 12th and
13th seconds respectively. The body starts

Let $\vec{v}$ and $\vec{a}$ denote the velocity and acceleration respectively of a body in one dimensional motion. Then correct option is

The deceleration experienced by a moving motorboat after its engine is cut off, is given by $\mathrm{dv} / \mathrm{dt}=-\mathrm{kv}^3$ where $\mathrm{k}$ is constant. If $\mathrm{v}_0$ is the magnitude of the velocity at cut-off, the magnitude of the velocity at a time $t$ after the cut-off is

The velocity vector of a particle moving over a horizontal plane is given by $\vec{v}=2 t \hat{i}$. The ratio of the magnitude of instantaneous acceleration of the particle at ${t}=2 \mathrm{sec}$ to the magnitude of displacement of the particle during the interval of first $2 \mathrm{sec}$ is

Statement-I: The average velocity of a particle is zero in a time interval. It is possible that the instantaneous acceleration is never zero in the interval.
Statement-II: The magnitude of average velocity in an interval is equal to its average speed in that interval.

The numerical ratio of displacement to the distance covered is always

Statement-I: The speed of a body can be negative.
Statement-II: If the body is moving in the opposite direction of positive motion, then its speed is negative.

Two particles are moving with velocities 17 m/sec and 14 m/sec along positive X-axis. Their initial positions are at x = 24 m, x = 120 m respectively. find time taken by first particle to cross second one

Assertion: For unidirectional movement of an object, displacement > distance.

Reason: For unidirectional movement of an object, displacement $=$ distance.

A train has a speed of 60 km/h. for the first one hour and 40 km/h for the next half hour. Its average speed in km/h is

If magnitude of average speed and average velocity over an interval of time are same, then

Assertion: The displacement-time graph of a body moving with uniform acceleration is a straight line.

Reason: The displacement is proportional to time for uniformly accelerated motion.

Two trains 101 m and 99 m in length are running in opposite direction with velocities 54 km/h and 36 km/h. In what time they will completely cross each other ?