A particle moving on a curve has the position at time t given by `x=f'(t) sint + f''(t) cost , y=f'(t) cost - f''(t) sin t` , where `f` is a thrice differentiable function. Then the velocity of the particle at time `t` is

f(x)=int_0^x e^t f(t)dt+e^x , f(x) is a differentiable function on x in R then f(x)=

A particle moving along x-axis has acceleration f , at time t , given by f = f_0 (1 - (t)/(T)) , where f_0 and T are constant. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0 , the particle's velocity (v_x) is :

Differentiate the function f(t)=sqrt(t)(1-t)

The x and y coordinates of a particle at any time t are given by x = 2t + 4t^2 and y = 5t , where x and y are in metre and t in second. The acceleration of the particle at t = 5 s is