The motion of a particle of mass m is given by x=0 for `t lt 0` s, x (t) = `A sin 4pit for 0 lt t(1//4) s (A gt 0)` and x=0 for `t gt (1//4)` s Which of the following statement(s) is (are) true?

The motion of a particle of mass m is given by x = 0 for t lt 0 s, x(t) = A sin 4pit for 0 lt t lt (1/4) s (A gt 0) and x =0 for t gt(1/4) s which of the following statements is true ?

The motion of a particle of mass m is given by x=0 for tlt0s , x(t)=Asin4pit for 0lttlt((1)/(4))s (Agt0) and x=0 for tgt((1)/(4))s .

The motion of a particle of mass m is given by x=0 for tlt0s , x(t)=Asin4pit for 0lttlt((1)/(4))s(Agt0) ,and x=0 for tgt((1)/(4))s .

The motion of a particle of mass m is given by x = 0 for t 0), and x = 0 for t > (1/4) s. which of the following statements is true?/

Shows the position-time graph of a particle of mass 4 kg. What is the (a) force on the particle for t lt 0, t gt 4 s, 0 lt t lt 4 s ? (b) impulse at t = 0 and t = 4 s ? (Consider one­dimensional motion only).

For x , t in R let p_(t) (x)= ( sin t) x^(2) - (2 cost ) x + sin t be a family of quadratic polynomials in x with variable coefficients. Let A(t) = int_(0)^(1) p_(t) ( x)dx , Which of the following statements are true? (I) A(t) lt 0 for all t. (II) A(t) has infinitely many critical points. (III) A(t) = 0 for infinitely many t. (IV) A'(t) lt 0 for all t.