Motion in a straight line practice · Mixed difficulty

Consider the acceleration, velocity and displacement of a tennis ball as it falls to the ground and bounces back. Directions of which of these changes in the process

If Position of a particle is given by $x=\left(4 t^2-8 t\right)$, then which of the following is true?

The numerical ratio of displacement to the distance covered is always

Assertion (A): Speed of a particle may decrease, even if acceleration is increasing.

Reason (R): This will happen if acceleration is positive.

A body is moving along a straight line path with constant velocity. At an instant of time the distance travelled by it is s and its displacement is D, then

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.

A particle moving with uniform acceleration has its final velocity $(v = \sqrt {150 + 8x} )\,\,m\mathrm{/}s$ where $x$ is the distance travelled by the body then the acceleration

A car travels equal distances in the same direction with velocities $60\mathrm{km}{\mathrm{h}^{ - 1}}\,,\,20\;\mathrm{km\;}{\mathrm{h}^{ - 1}}$ and $10\;\mathrm{km\;}{\mathrm{h}^{ - 1}}$ respectively. The average velocity of the car over the whole journey of motion is

Two particles are moving with velocities 22 m/sec and
3 m/sec along X-axis in opposite direction. Their initial
positions are at x = 30 m, x = 180 m respectively. find
time interval after which they meet with each other

The velocity of light in vaccum is $3 \times {10^8}\,m/s$. Calculate the time taken by it to travel a distance of $6 \times {10^{14}}\,m$

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

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

Stopping distance of a moving vehicle is directly proportional to

A man goes 10 m towards North, then 20 m towards east then displacement 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

Velocity of a body on reaching the point from which it was projected upwards, is

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

In one dimensional motion, instantaneous speed $v$ satisfies $0 \leq v < v_0$.

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

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

The relative velocity $\mathrm{V}_{\mathrm{AB}}$ or $\mathrm{V}_{\mathrm{BA}}$ of two bodies $\mathrm{A}$ and $\mathrm{B}$ may be

I. greater than velocity of body A

II. greater than velocity of body B

III. less than the velocity of body A

IV. less than the velocity of body B

The x and y coordinates of a particle at any time $t$ are given by $x = 8{t^2} + 5{t^3}$ and $y = 2t$. Where x and y are in metre and $t$ in seconds. The acceleration of particle at $t = 5$ sec is

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

A police jeep is chasing with velocity of $45 \mathrm{~km} / \mathrm{h}$ a thief in another jeep moving with velocity $153 \mathrm{~km} / \mathrm{h}$. Police fires a bullet with muzzle velocity of $180 \mathrm{~m} / \mathrm{~s}$. The velocity with which it will strike the car of the thief is

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

Two bodies move in a straight line towards each other with initial velocities $v_1$ and $v_2$ and with constant accelerations $a_1$ and $a_2$ directed against their corresponding initial velocities. The maximum initial separation $\ell_{\max }$ between them for which they will meet during the motion is:

Assertion : Displacement of a body is vector sum of the area under velocity- time graph.

Reason : Displacement is a vector quantity.

A ball is thrown vertically upwards. It was observed at a height h twice with a time interval $\Delta$t. The initial velocity of the ball is

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