Motion in a straight line practice · Medium

The acceleration of a particle increasing linearly with time t is bt. The particle starts from the origin with an initial velocity ${v_0}$. The distance travelled by the particle in time t will be

Which of the following is a one dimensional motion?

A particle comes round a circle of radius 1 m once. The time taken by it is 10 sec. The average velocity of motion is

Assertion: A lift is ascending with decreasing speed means acceleration of lift is downwards.
Reason: A body always moves in the direction of its acceleration.

An engine of a train moving with uniform acceleration passes the signal-post with velocity $u$ and the last compartment with velocity $v$. The velocity with which middle point of the train passes the signal post is

A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

Assertion: Doubling the initial velocity, the stopping distance of moving object increases by a factor of 4 (for the same deceleration).
Reason: Stopping distance is proportional to the square of the initial velocity.

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

Statement I: Only single value of distance is possible between two fixed points.

Statement II: Infinite values of displacements are possible between two fixed points.

A body start from rest and moves with constant acceleration. The ratio of distance covered by the body in $n\,{\text{th}}$ second to that covered in $n$ second is

A ball of mass $m$ and another ball of mass $2 m$ are dropped from equal heights. If the time taken by the balls to reach the ground are $t_1$ and $t_2$ respectively, then (neglect air drag)

From the top of a tower of height 50m, a ball is thrown vertically upwards with a certain velocity. It hits the ground 10 s after it is thrown up. How much time does it take to cover a distance AB where A and B are two points 20m and 40m below the edge of the tower? ($\mathrm{g} = 10\mathrm{m}{\mathrm{s}^{ - 2}}$)

A particle covers 4m, 5m, 6m, and 7m, in 3rd, 4th, 5th and 6th second respectively. The particle starts

The position of a particle moving along $x$-axis varies with time $t$ as $4 x+t^2=4$. At what position, the particle is at rest?

A particle moves in a straight line so that its displacement x metre at time t second is given by
$t = \sqrt {{x^2} - 1}$ Its acceleration in $\mathrm{m}{\mathrm{s}^{ - 2}}\mathrm{\;}$ at time t second is

A body is projected with a velocity 60 m/s vertically upwards the distance travelled in last second of its motion $[g = 10\,\,m\mathrm{/}{s^2}]$

The motion of a particle along a straight line is described by the equation: $x=8+12 t-t^3$, where ${x}$ is in meter and ${t}$ in second.

(i) the initial velocity of particle is $12 \mathrm{~m} / \mathrm{s}$

(ii) the retardation of particle when velocity is zero is $12 \mathrm{~m} / \mathrm{s}^2$

(iii) when acceleration is zero, displacement is $8 \mathrm{~m}$

(iv) the maximum velocity of particle is $12 \mathrm{~m} / \mathrm{s}$

Assertion: The magnitude of average velocity of an object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.
Reason: Path length (distance) is either equal to or greater than the magnitude of displacement.

A particle starts from rest and moving with constant acceleration. Let ${S}_{{n}}$ and ${S}_{{n}+1}$ be the distance travelled by the particle in the time intervals ${t}={n}-1$ to ${t}={n}$ and ${t}={n}$ to ${t}={n}+1$ respectively. The ratio $\frac{S_n}{S_{n+1}}$ is :

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)

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