Motion in a straight line practice · Mixed difficulty

A man is sitting in a train which is moving with a velocity of $60 {~km} / {h} o u r$. His speed with respect to the train is:

Two ends of a train moving at constant acceleration pass a point with speed of $12 \mathrm{~m} / \mathrm{s}$ and $24 \mathrm{~m} / \mathrm{s}$ respectively. The speed with which middle point of the train passes the same point is (approximately)

A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after ${t_1}$ and ${t_2}$ seconds respectively, then

Which of the following statements is not correct?

Two spheres of same size, one of mas 2 kg and another of mass 4 kg, are dropped simultaneously from the top of Qutub Minar (height =72m). When they are 1 m above the ground, the two spheres have the same

A particle moving along a straight line has a velocity $v\;\mathrm{m}{\mathrm{s}^{ - 1}}$, when it cleared a distance of y metre. These two are connected by the relation $v = \sqrt {49 + y}$. When its velocity is 1 $\mathrm{m}{\mathrm{s}^{ - 1}},$, its acceleration (in $\mathrm{m}{\mathrm{s}^{ - 2}}$)is

A stone is thrown vertically upward with a speed of $28 \mathrm{~m} / \mathrm{s}$. (a) Find the maximum height reached by the stone. (b) Find its velocity one second before it reaches the maximum height?

A body of mass $2kg$ has an initial velocity of $3m/s$ along $x - axis$ and it is subjected to an acceleration of $2\,m/{s^2}$ in Y-direction. The distance of the body from origin after $4s$ will be

Two bodies of different masses are dropped from heights of 16 m and 25 m respectively. The ratio of the time taken by them to reach the ground 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

A body is moving from rest under constant acceleration and let ${S_1}$ be the displacement in the first (P-1) sec and ${S_2}$ be the displacement in the first P sec. The displacement in ${\left( {{P^2} - P + 1} \right)^{th}}$ see will be

A driver takes $0.20 \mathrm{~s}$ to apply the brakes after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of $54 \mathrm{~km} / \mathrm{h}$ and the brakes cause a deceleration of $5.0 \mathrm{~m} / \mathrm{s}^2$, find the distance travelled by the car after he sees the need to put the brakes on.

The initial velocity of a body moving along a straight line is 7 m/s. It has a uniform acceleration of $4\;m/{s^2}$. The distance covered by the body in the $\;{5^{th}}$ second of its motion is

Car $A$ is moving with a speed of $36 \mathrm{~kmh}^{-1}$ on a two lane road. Two cars $B$ and $C$, each moving with a speed of $54 \mathrm{~kmh}^{-1}$ in opposite directions on the other lane are approaching car A. At certain instant of time, when the distance $A B=A C=1 \mathrm{~km}$, the driver of car $B$ decides to overtake $A$ before $C$ does. What must be the minimum acceleration of car $B$, so as to avoid an accident ?

A particle moves along a straight line such that its position x at any time t is $x = 6{t^2} - {t^3}.$. Where x in metre and t is in second, then

Two bodies one held $100 \mathrm{~cm}$ directly above the other are released simultaneously from the large height and both fall freely under the gravity. The separation between the bodies just after $2 \mathrm{~s}$ will be

The velocity of a body at a given instant of time during motion is:

Two trains travelling on the same track are approaching each other with equal speeds of $40\mathrm{m}{\mathrm{s}^{ - 1}}$. The drivers of the trains begin to decelerate simultaneously when they are just 2 km apart. If the decelerations are both uniform and equal, then the value of deceleration to barely avoid collision should be

If position vector of a particle at time $t$ is $\vec{r}=3 t \hat{i}+(8-4 t) \hat{j} \mathrm{~m}$, then

Which of the following 4 statements is false

A cyclist moving on a circular track of radius 40 m completes half a revolution in 40 s. Its average velocity is

An object is moving with uniform acceleration. Its velocity after 5 seconds is $25 \mathrm{~ms}^{-1}$ and after 8 seconds, it is $34 \mathrm{~ms}^{-1}.$ Find the distance travelled by the object in 12th second.

A body is dropped from the top of a tower clears ${\left( {7/16} \right)^{\mathrm{th}}}$ of total height of the tower in its last second of flight. The height of the tower is

Assertion: For a particle, acceleration-time graph gives the velocity.
Reason: Rate of change of velocity is acceleration.

A particle covers equal distance around a circular path, in equal intervals of time. Which of the following quantities connected with the motion of the particle remains constant with time?

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 $PQ = QR$

Two cars A and B at rest at same point initially. If A starts with uniform velocity of 40 m/sec and B starts in the same direction with constant acceleration of $4m/{s^2}$, then B will catch A after how much time

I. Particle-1 is dropped from a tower and particle-2 is projected horizontal from the same tower, then both the particles reach the ground simultaneously.

II. Both the particles strike the ground with different speeds.

Which of the following statement(s) is/are correct?

A particle moves along a straight line such that its displacement at any time t is given by $S = {t^3} - 6{t^2} + 3t + 4$ metres. The velocity when the acceleration is zero is

A moving car possesses average velocities of 5 m/s, 10 m/s and 15 m/s. In the first, second and third seconds respectively. Then the total distance covered by the car in these 3 seconds is