PHYSICS A catapult used to hold a stone of mass 500g is extended by 20cm with an applied force F . If the stone leaves with a velocity of 40ms^(-1) , the value of F is A. 4.0 xx10^(4)N C. 2.0 xx10^(3)N B. 4.0 xx10^(3)N D. 4.0 xx10^(2)N m+500,=0.5ks e=20cmquadc_(0)=0.2m v=arm-1^(-1) The frictional force is independent of the area of the surfaces in contact. The frictional force depends on the nature of the surfaces in contact. III. The frictional force depends on the speed of sliding. IV. The frictional force is directly proportional to the normal reaction. Which combination of the above is true of sliding friction? A. I, II and IV C. I, III and IV B. I, II and III D. II, III and IV The velocity v of a particle in a time t is given by the equation v=10+2t^(2) Find the instantaneous acceleration after 5 seconds. sqrtv=10+2l^(2) A. 10ms^(-1) B. 15ms^(-1) C. 20ms^(-1) D. 60ms^(-1) sqrt=+0+2xx5^(2) 4. If the force and the velocity on a system are each reduced simultaneously by half, the power of the system is A. Doubled ℓ . Reduced to a quarter B. Constant Đ. Reduced by half 5. The velocity ratio of a machine is 5 and its efficiency is 75% . What effort would be needed to lift a load of 150N with the machine? A. 50N B 40N C. 30N D. 20N

1. Using the work-energy principle, , where is the spring constant, is the extension, is the mass, and is the velocity, we get .2. The true statements about sliding friction are I, II, and IV.3. To find the instantaneous acceleration, we need to differentiate the velocity with respect to time: . Substituting , we get .4. If both force and velocity are halved, the power will be reduced to a quarter since power is directly proportional to the force and the velocity.5. The effort required can be found using the formula for the mechanical advantage: .