An automobile is moving on a horizontal road with a speed of v.If teh coeficient of friction between the tyres nd the road is `mu`,show that the shortest distance in whih the automobie can be stopped is `v^2l2mug`.

Figure 5.18 shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s^-2 . What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt ? (Mass of the man = 65 kg.)

The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown. The coefficient of friction between the box and the surface below its is 0.15. On a straight road, the truck starts from rest and accelerates with 2 ms^-2 . At what distance from the starting point does the box fall off the truck ?/ (Ignore the size of the box).

When a car moving with 36 km h^(-1) reaches an upward inclined road of angle 30^@ ,its engine is switched off.If the co-efficient of friction is 0.1,how much distance will the car move before coming to rest ?(Take = 10 m s^(-2) ).

A hill is 500 m high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of 125 m//s over the hill. The canon is located at a distance of 800m from the foot of hill and can be moved on the ground at ba speed of 2 m//s, so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill? Take g= 10 m//s^(2) .

The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Fig. 5.22. The coeffcient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 m s^-2 . At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

A particle of mass m and charge (-q) enters the region between the two charged plates initially moving along x-axis with speed v_x. The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL^2//(2m v_x^2) .