Motion in A Str...

Which of the following statements is correct for a particle travelling with a constant speed?

A car and a bike start racing in a straight line. The distance of the finish line from the starting line is $$100m$$. The minimum acceleration of the car for it to win, if it accelerates uniformly starting from rest and the bike moves with a constant velocity of $$10m/s$$, is

A particle starts moving along a line from rest and comes to rest after moving distance $$d$$. During its motion, it had a constant acceleration $$f$$ over $$2/3$$ of the distance and covered the rest of the distance with constant retardation. The time taken to cover the distance is:

A train of length / = 350 m starts moving rectilinearly with constant acceleration a = $$3.0 \times 10^{-2}$$ $$ms^{-2}$$. After r = 30 s from start, the locomotive headlight is switched on (event 1), and 60 s after this event, the tail signal light is switched on (event 2).
a.Find the distance between these events in the reference frame fixed to the train and to the Earth.
b.How and at what constant velocity v relative to the Earth must a certain reference frame R move for the two events to occur in it at the same point?

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

Two cars are travelling towards each other on a straight road at velocities $$15ms^{-1}$$ and $$16ms^{-1}$$ respectively. When they are $$150$$m apart, both the drivers apply the breaks and the cars decelerates at $$3ms^{-2}$$ and $$4ms^{-2}$$ until they stop. How for apart will they be when they have come to a stop.

A man running with a uniform speed 'u' on a straight road observes a stationary bus at a distance 'd' ahead of him. At that instance , the bus starts with an acceleration 'a' .The condition that he would be able to catch the bus is:

A body is falling freely from a point $$A$$ at a certain height from the ground and passes through points $$B,C$$ and $$D$$ (vertically as shown) so that $$BC=CD$$. The time taken by the particle to move from $$B$$ to $$C$$ is $$2$$ seconds and from $$C$$ to $$D$$ $$1$$ second. Time taken to move from $$A$$ to $$B$$ in seconds is

The maximum height reached by the ball as measured from the ground would be:

The maximum separation between the floor of elevator and the ball during its flight is: