The increase in the speed of a car is proportional to the additional petrol put into the engine. Is it possible to accelerate a car without putting more petrol or less petrol into the engine?

A sports car accelerations from zero to a certain speed in t seconds. How long does it take for it to accelerate to twice that speed starting from rest, assuming the power of the engine to be constant (independent of velocity) and neglecting any resistance to motion?

A man rides his motorcycle at the speed of 50 km/hour. He has to spend Rs. 2 per km on petrol. If he rides it at 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.

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field vecE. Due to the force q vecE, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more second under the influence of this filed. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively,

On complete combustion a litre of petrol gives off heat equivalent to 3 xx 10^(7) J. In a test drive, a car weighing 1200 kg including the mass of driver, runs 15 km per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform. calculate the force of friction acting on the car during the test drive. if the efficiency of the car engine were 0.5.

A car is moving on circular path of radius 100m such that its speed is increasing at the rate of 5m//s^(2) . At t=0 it starts from rest. What is the radial acceleration of car at the instant it makes one complete round trip ?

Car A of mass 1000 kg moves on a horizontal straight road with speed 36kmh^(-1) . If the force resisting the motion is 100 N, then find the power of the engine. Now, after covering 200 m distance, car A collides with a stationary car B of same mass and becomes stationary. As a result car B start moving on the horizontal road, then what would be the speed of car B just after the collision? (The engine of car B is off.)

The angular speed of a motor wheel is increased from 600 rpm to 1560 rpm in 8 seconds. (i) What is its angular acceleration, assuming the acceleration to be uniform? (ii) How many revolutions does the engine make during this time?