Motion in a straight line practice · Mixed difficulty

Two trains, each of length $100 \mathrm{~m}$, are running on parallel tracks. One overtakes the other in $20 \mathrm{sec}$. and one crosses the other in opposite direction 10 sec. Calculate the velocities of each train.

A point moves in a straight line, so that its displacement $x$ at time $t$ is given by $x^2=t^2+1$. Its acceleration is

A particle moves according to the equation $\frac{d v}{d t}=\alpha-\beta v$, where $\alpha$ and $\beta$ are constants. Find velocity as a function of time. Assume, body starts from rest

The numerical ratio of displacement to distance for a moving object is

Two bodies are held separated by $9.8 \mathrm{~m}$ vertically ane above the other. They are released simultaneously to fall freely under gravity. After $2 \mathrm{~s}$, the relative distance between them is

The numerical ratio of displacement to distance is

Velocity – time graph of a body thrown vertically up is

If $V=\alpha \sqrt{x}, \mathbf{V}$ is velocity, $\mathbf{x}$ is position, $\mathbf{a}$ is +ve constant then $\mathbf{a}=$ ?

The velocity $\mathrm{v}$ of a particle is given by the equation $v=6 t^2-6 t^3$ where $v$ is in $\mathrm{m} / \mathrm{sec}$ and $\mathrm{t}$ is time in seconds then :

A particle moves in a straight line as $s = \alpha \left( {t - 4} \right) + \beta {\left( {t - 4} \right)^2}$. Find the initial velocity and acceleration.

A particle is moving in a straight line. The variation of position '$x$' as a function of time '$t$' is given as $x=\left(t^3-6 t^2+20 t+15\right) {m}$. The velocity of the body when its acceleration becomes zero is

Which of the following statements, is incorrect regarding motion of particle along straight line?

If an object is falling freely in vacuum, then body moves with

Statement-I: In successive time intervals if the average velocities of a particle are equal then the particle must be moving with constant velocity.
Statement-II: When a particle moves with uniform velocity, its displacement always increases with time.

The velocity-time graph of particle comes out to be a non-linear curve. The motion is

What determines the nature of the path followed by the particle

A body $P$ is thrown vertically up with velocity 30 m/s and another body $Q$ is thrown up along the same vertically line with the same velocity but 1 second later from the ground. When they meet $\left( {g = 10\,m/{s^2}} \right)$

A man leaves his house for a cycle ride. He comes back to his house after half-an-hour after covering a distance of one $\mathrm{km}$. What is his average velocity for the ride?

A particle is thrown vertically upward with speed 45 m/s. Find the distance covered by the particle in the 5th second of its journey.

If a body is moving along a straight path then which of the following is true?

If $f=f_0\left[1-\frac{t}{T}\right]$, where $f=$ acceleration at time $t$ then find value of $v$ at $t=t$. when $\mathbf{t}=\mathbf{0}, \mathbf{u}=\mathbf{0}$

A particle starts from rest at the point $A(1,2,-3) {m}$ and reaches at the point $B(3,4,5) {m}$. The magnitude of displacement of man is

Which branch of physics deals with motion without considering its causes?

A ball is thrown vertically upwards with a speed of 20 m/s from the top of a tower 250 m height and another is thrown vertically downwards with the same speed simultaneously. The time difference between them $m$ reaching the ground is

A plane travelling north at $200 \mathrm{~m} / \mathrm{s}$ turns and then travels south at $200 \mathrm{~m} / \mathrm{s}$. Its change in velocity is:

A stone is allowed to fall from the top of a tower 100m high and at the same time another stone is projected vertically upwards from the ground with a velocity of $254\mathrm{m}{\mathrm{s}^{ - 1}}$. The two stones will meet after

A body is projected up with a speed ‘u' and the time taken by it is T to reach the maximum height H. Pick out the correct statement

A particle under the action of a constant force moves from rest upto 20 seconds. If distance covered in first 10 seconds is $\mathrm{S}_1$ and that covered in next 10 seconds in $\mathrm{S}_2$, then

A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is

Three ships A, B and C are in motion. The motion of A as seen by B is with speed V towards the north-east. The motion of B as seen by C is with speed V towards the north-west. Then, as seen by A, C will be moving towards the