The cost of fuel for running a bus is proportional to the square of the speed generated in km/h. It cost Rs 48 per hour when the bus is moving with a speed of 20 km/h. What is the most economical speed if the fixed charges are Rs 108 for one hour, over and above the running charges?

A car takes 2 hours to reach a destination by travelling at the speed of 60 km/h. How long will it take when the car travels at the speed of 80 km/h?

Assuming that the petrol burnt per hour in driving a motor boat varies as the cube of its velocity, show that the most economical speed when going against a current of c km/hour is (3c)/(2) km/hour.

Two parallel rail tracks run north-south. Train A moves north with a speed of 54 km h^-1 and train B moves south with a speed of 90 km h^-1 . What is the relative velocity of B with respect to A

A bird is tossing (flying to and fro 0 between two cars moving towards each other on a straight road. On car has a speed of 18 km /h while the other has the speed of 27 km /h. The bird starts moving from first caer towards the other and is moving with the speed of 36 km /h and when the two cars were separated by 36 km. What is the total distance comered by the bird ? What is the total displacement of the bird ?

A car A is travelling on a straight level road with a uniform speed of 60 km/h. It is followed by another car B which in moving with a speed of 70 km/h. When the distance between then is 2.5km, the car B is given a deceleration of 20km//h^2 . After how much time will B catch up with A

A man rides his motorcylcle at the speed of 50 km/hour. He has to spend Rs.2 per km on petrol. If the rides it as a faster speed of 80 km/hour, the petrol cost increases to Rs.3 per km. he has atmost Rs.120 to spend on petrol and one hour's time, He wishes to find the maximum distance that he can travel Express this problem as a linear programming problem and solve it graphically to find the maximum distance he can travel.

On a long horizontally moving belt (Fig. 3.26), a child runs to and fro with a speed 9 km h^-1 (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h^-1 . For an observer on a stationary platform outside, what is the:- speed of the child running opposite to the direction of motion of the belt ?

On a long horizontally moving belt (Fig. 3.26), a child runs to and fro with a speed 9 km h^-1 (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h^-1 . For an observer on a stationary platform outside, what is the:- speed of the child running in the direction of motion of the belt ?.