Ablock of mass m is at rest at the origin at t = 0. it is pushed with constant force fo from x= 0 to x=l across a horizontal surface whose coefficient of kinetic friction is μk = μo (1-x/l) that is, the coefficient of friction decreases from μo at x=0 to zero at x= l. we would like to know the velocity of the block when it reaches some position x. finding this requires an integration. however, acceleration is defined as a derivative with respect to time, which leads to integrals with respect to time, but the force is given as a function of position. to get around this, use the chain rule to find an alternative definition for the acceleration ax that can be written in terms of vx and dvxdx.

50 inches should be the resultant vector

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.