Motion in A Str...

Particle is moving in a straight path with an acceleration $$ a = bt^n $$, where b is a positive constant $$ \left( n\neq -1 \right)  $$. The relation between the velocity and the position vector of the particle at time t = 1s [Assuming particle is in rest at origin at t=0]

A body travels 200 cm in the first two seconds and 220 cm in the next 4 seconds with same acceleration. The velocity of the body at the end of the 7th second is:

a ship of mass $$3\times 10^{7}$$ kg initially at rest is pulled by a force of $$5\times 10^{4}$$ N through a distance of 3 m. Assuming that the resistance due to water is negligible, what will be the speed of the ship ?

A body of mass $$2\ kg$$ fall vertically, passing through two points $$A$$ and $$B$$. The speeds of the body as it passes $$A$$ and $$B$$ are $$1\ m/s$$ and $$4\ m/s$$ respectively. The resistance against which the body falls is $$9.6\ N$$. What is the distance $$AB$$?

A parachutist after bailing  out falls $$50 m$$ without friction. When parachute opens, it decelerate at $$2 m/s^2$$. He reaches the ground with a speed of $$3 m/s$$. At what height, did he bail out nearly.

A body is through 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 then

A ball, thrown by a boy, is caught by another boy in 2s. What is the maximum height attained by the ball?

If you decide to launch a ball vertically to a friend located 45 m above you who  can catch it. What is the minimum launch speed you can use?

A bus begins to move with an acceleration of $$\dfrac{1}{2} \,m/s^2$$. A person who is $$40 \,m$$ behind the bus, runs at a rate of $$7 \,m/s$$. Find the time taken by the person to catch the bus.

A stone is allowed to fall freely from rest. The ratio of the time taken to fall through the first meter and the second meter distance is :