A train moving with uniform acceleration has its front end passing a given fixed point P with a speed u and the tail end passing the same point P with a speed v . What is the speed of the mid -point of the train when passing the point ?

A body moving with uniform acceleration has velocity of 20m/s and 30 m/s when passing point P with Q in its path . Find its velocity at the point midway between P and Q .

If P is the point (2,1,6), then find the point Q such that PQ is perpendicular to the plane passing through the points (2,1,0), (5,0,1), (4,1,1) and the mid point of PQ lies on it.

A body travels from a point P to point Q by the shortest route with a velocity of 50km/h and returns to P by the same route with a velocity of 70 km/h. What is the average speed ?

Starting from the rest , a body P travels with a uniform acceleration of 4m/s^2 and starting from rest from the same point 4s later , a body Q travels with a uniform acceleration of 16m/s_2 in the same direction as P . Find when and where they meet .

Show that the relation R on the set A of points in a plane given by R ={(P,Q): distance of the point P from the origin is same as the distance of the point Q from the origin) is an equivalence relation. Further, show that the set of all points related to a point P ne (0,0) is the circle passing through P with origin as centre.

Find the equation of a curve passing through the point(0,-2),given that at any point(x,y)of the curve,the product of the slope of its tangent and y-cordinate of the point is equal to the x co-ordinate of the point.