A cone falling with a speed `v_(0)` strikes and penetrates the block of a packing material. The acceleration of the cone after impact is
`a=g-cx^(2)`. Where c is a positive constant and x is the penetration distance. If maximum penetration depth is `x_(m)` then c equals

A bullet with a speed of 3 x 10^3 cm//s strikes a wooden target and penetrates a distance of 1.5 cm. Find (i) the acceleration (ii) the time.

If f(x)=a+bx^(2)+cx^(4)+dx^(6), where a,b,c,d all are positive constants, then

A bullet of mass m travelling horizontally with speed u strikes a wooden block of mass 'M' placed on a smooth horizontal plane. The penetration is assumed uniform and the bullet comes to rest after penetrating a distance 'd' into the block. Then choose the correct statement :

if int x^(5)e^(-x^(2))dx=g(x)e^(-x^(2))+c where c is a constant of integration then g(-1) is equal to

The velocity upsilon of a particle as a function of its position (x) is expressed as upsilon = sqrt(c_(1)-c_(2)x) , where c_(1) and c_(2) are positive constants. The acceleration of the particle is

The velocity upsilon of a particle as a function of its position (x) is expressed as upsilon = sqrt(c_(1)-c_(2)x) , where c_(1) and c_(2) are positive constants. The acceleration of the particle is

The speed v of a car moving on a straight road changes according to equation, v^2 = 1 + bx , where a and b are positive constants. Then the magnitude of acceleration in the course of such motion : (x is the distance travelled).