Motion in a straight line practice · Medium

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

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

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.

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

A particle is thrown vertically up with an initial velocity $9 \mathrm{~m} / \mathrm{s}$ from the surface of Earth (take $g=10 \mathrm{~m} / \mathrm{s}^2$). The time (in seconds) taken by the particle to reach a height of $4 \mathrm{~m}$ from the surface second time (in seconds) is

A particle is constrained to move on a straight line path. It returns to the starting point after $10 \mathrm{~s}$. The total distance covered by the particle during this time is $30 \mathrm{~m}$. Which of the following statements about the motion of the particle is true?