Motion in A Str...

A ball is projected vertically up with a velocity of $$40$$ $$m/s$$. At the same time another ball is dropped from a height of $$100$$ m. The magnitudes of their velocities are equal after a time of $$(g= 10m/s^{2})$$

A car, starting from rest, accelerates at the rate $$f$$ through a distance $$S$$, then continues at constant speed for time $$t$$ and then decelerate at the rate $$\frac{f}{2}$$ to come to rest. If the total distance travelled is $$15S$$, then

A point moves with uniform acceleration. Let $$v_{1}$$, $$v_{2}$$, $$v_{3}$$ denote the average velocities in three successive intervals of time $$t_{1}$$, $$t_{2}$$, $$t_{3}$$. Correct relation among the following is

A man in a lift ascending with an upward acceleration throws a ball vertically upwards and catches it after $$t_{1}$$ second. Later when the lift is descending with the same acceleration, the man throws the ball up again with same velocity and catches it after $$t_{2}$$ second.
A) The acceleration of the elevator is $$g\dfrac{(t_{2}-t_{1})}{(t_{1}+t_{2})}$$
B) The velocity of projection of the ball relative to elevator is $$\dfrac{t_{2}t_{1} g}{t_{1}+t_{2}}$$.
We can conclude that:

A body is thrown vertically upwards with an initial velocity $$u$$ reaches a maximum height in $$6s$$. The ratio of the distance travelled by the body in the first second to the seventh second is

A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x-direction with a constant speed. The position of the first body is given by $$x_{1}(t)$$ after time t and that of the second body by  $$ x_{2} (t)$$ after the same time interval. Which of the following graphs correctly describes $$( x_{1} - x_{2})$$ as a function of time t ?

An object falls from a bridge that is $$45\ m$$ above water. It falls directly into a small boat moving with constant velocity that is $$12\ m$$ from the point of impact when the object was released. The speed of the boat is

A body, projected vertically upwards, crosses a point twice its journey at a height $$h$$ just after $$t_{1}$$ and $$t_{2}$$ seconds. Maximum height reached by the body is

A train is moving forward at a velocity of $$2.0$$ $$m/s$$. At the instant the train begins to accelerate at $$0.80  m/s^{2}$$, a passenger drops a coin which takes $$0.50\ s$$ to fall on the floor. Relative to a spot on the floor directly under the coin at release, the coin lands

A ball is thrown vertically upwards with a velocity $$u$$ from the balloon descending with velocity $$v$$. The ball will pass by the balloon after time