Motion in a straight line practice · Medium

For a body moving with relativistic speed, if the velocity is doubled, then

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.

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 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

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

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.

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 ?

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 $g=10 \mathrm{~ms}^{-2}$ ]