Motion in a straight line practice · Mixed difficulty

A car accelerates from rest at a constant rate $\alpha$ for some time, after which it decelerates at a constant rate $\beta$ comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is

A body moving with a uniform acceleration crosses a distance of 65 m in the 5th second and 105 m in 9th second. How far will it go in 20 s?

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

A particle covers half of its total distance with speed ${v_1}$ and the rest half distance with speed ${v_2}$. Its average speed during the complete journey is

A police jeep is chasing a culprit going on a motor bike. The motor bike crosses a turning at a speed of 72 km/h. The jeep follows it a speed of 90 km/h crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike? (in km)

Assertion: The average speed of a body over a given interval of time is equal to the average velocity of the body in the same interval of time if a body moves in a straight line in one direction.
Reason: Because in this case distance travelled by a body is equal to the displacement of the body.

An object is projected upwards with a velocity of 100m/s. It will strike the ground after (approximately)

The three initial and final position of a man on the x-axis are given as (i) (-8m,7m) (ii) (7m,-3m) and (iii) (-7m,3m) Which pair gives the negative displacement

Two balls are projected upward simultaneously with speeds of $40 {~m} / {s}$ and $60 {~m} / {s}$. Relative distance of the second ball with respect to the first ball at time $t=5 {sec}$ will be [Neglect air resistance]

A ball dropped from a point $P$ crosses a point $Q$ in $t$ seconds. The time taken by it to travel from Q to R, if $PQ = QR$

An insect moves $3m\,\,east$, $4m\,\,north$ and $5m$ vertically up. Displacement covered by insect is

A particle moves in the east direction with 15 m/sec for 2 sec then northwards with 5 m/s for 8 sec. Average speed of the particle is

Select the incorrect statements from the following
S1 : Average velocity is path length divided by time interval
S2 : In general, speed is greater than the magnitude of the velocity
S3 : A particle moving in a given direction with a non-zero velocity can have zero speed
S4 : The magnitude of average velocity is the average speed

Assertion: Kinematic equations are exact and are always correct.
Reason: The definitions of instantaneous velocity and acceleration are true only for motion in which the magnitude and direction of acceleration are constant during motion.

If distance covered by a particle is zero, what can you say about its displacement?

A body is thrown vertically upward from a point $A$ $125 \mathrm{~m}$ above the ground. It goes up to a maximum height of $250 \mathrm{~m}$ above the ground and passes through $A$ on its downward journey. The velocity of the body when it is at a height of $70 \mathrm{~m}$ above the ground is (Take, $g=10 \mathrm{~ms}^{-2}$ )

An automobile, travelling at 40 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is (assume no skidding)

A body travels $102.5 \mathrm{~m}$ in ${n}^{\text {th}}$ second and $115.0 \mathrm{~m}$ in $({n}+2)^{\mathrm{th}}$ second. The acceleration is:

For a body travelling with uniform acceleration, its final velocity is $V = \sqrt {180 - 7x}$, where $x$ is the distance travelled by the body then the acceleration is

A car travels half the distance with constant velocity of 40 kmph and the remaining half with a constant velocity of 60 kmph. The average velocity of the car in kmph is

A ball thrown vertically upwards after reaching a maximum height h, returns to the starting point after a time of l0 s. Its displacement is

STATEMENT-1 : For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

STATEMENT-2 : If the observer and the object are moving at velocities $\vec{v}_1$ and $\vec{v}_2$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $\vec{v}_2-\vec{v}_1$.

A body falls for 5 s from rest. If the acceleration due to gravity of earth ceases to act, the distance it develops in the next 3 s is

A particle moves along x-axis as $x = 4\left( {t - 2} \right) + a{\left( {t - 2} \right)^2}$ Which of the following is true

The displacement of a body along X- axis depends on time as $\sqrt x = t + 1.$ Then the velocity of body

The position of a particle x (in metres) at a time t seconds is given by the relation $\vec r = \left( {3t\hat i - {t^2}\hat j + 4\hat k} \right)$. Calculate the magnitude of velocity of the particle after 5 seconds

A stone falls from a balloon that is descending at a uniform rate of $12\mathrm{m}{\mathrm{s}^{ - 1}}$. The displacement of the stone from the point of release after 10s is

A body having an initial velocity of $10\,\,\,m{s^{ - 1}}$ moves with a uniform acceleration $20\,\,\,m{s^{ - 2}}$ and reaches a final velocity $v = 40\,\,\,m{s^{ - 1}}$ in 4 seconds. The acceleration of the body is $\left[ {m{s^{ - 2}}} \right]$

A body thrown vertically upward with an initial velocity of 1.4 m/s returns in 2s. The total displacement of the ball is

A particle moving along $X$-axis has acceleration $f$, at time $t$, given $f=f_0\left(1-\frac{t}{T}\right)$, where $f_0$ and $T$ are constants. The particle at $t=0$ has zero velocity. When $f=0$, the particle's velocity $\left(v_x\right)$ is