Joseph jogs from one end to the other end B of a straight 300m road in 2minutes 30 seconds and then turns around and jogs 100m back to point C in another 1minute. What are Joseph's average speeds and velocities in jogging (a) from A to B and (b) from A to C?

A simple pendulum moves from one end to the other in 1/2 second. What is the frequency?

Usha swims in a 90 m long pool. She covers 180 m in one minute by swimming from one end to the other and back along the same length path. Find the average speed and average velocity of Usha.

A trolley of mass 200 kg moves with a uniform speed of 36 km//h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s^-1 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley ? How much has the trolley moved from the time the child begins to run ?

An arch is in the form of a semi-ellipse. It is 8m wide and 2m high at the centre. Find the height of the arch at a point 1.5 m from one end.

Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, how much string does she have out ? If she pulls in the string at the rate of 5 cm per second, what will the horizontal distance of the fly from her after 12 seconds ? .

A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90cm to 20cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg m^2 :- What is his new angular speed? (Neglect friction.)

A motorcylist drives from A to B with a unit speed of 30 kmh^-1 and returns back with a of 20 kmh^-1 . Find its average speed.