(6 marks) QUESTION TWO (15 Marks) (a) A particle moves along the curve x=t, y=t^2 and z=t^3 where t is the time. Find the components of its velocity and acceleration at time t=1 (b) The acceleration of a particle is given by (5 marks) (d^2overrightarrow (r))/(dt^2)=(3cos(3t))hat (i)+(3sin(3t))hat (j)+that (k) If overrightarrow (V) is zero at t=0 , find overrightarrow (V) at any time. (5 marks) (c) Find the angle between A=2i+2j-k and

Let's solve each part of the question step by step.### Part (a)A particle moves along the curve , , and where is the time. We need to find the components of its velocity and acceleration at time .**Velocity:**The velocity vector is given by the derivative of the position vector \(\overrightarrow{r}(t)\) with respect to time . Taking the derivative with respect to : At : So, the components of the velocity at are , , and .**Acceleration:**The acceleration vector is given by the derivative of the velocity vector \(\overrightarrow{v}(t)\) with respect to time . At : So, the components of the acceleration at are , , and .### Part (b)The acceleration of a particle is given by: If is zero at , we need to find at any time .To find \(\overrightarrow{V}(t)\), we integrate the acceleration vector with respect to time : Integrating each component separately: Given that \(\overrightarrow{V}(0) = 0\): Thus, ### Part (c)Find the angle between and .First, we need the dot product of and : Next, we need the magnitudes of and : The cosine of the angle between and is given by: Since is not specified, we cannot compute the exact angle without knowing . If were provided, we would substitute the values into the formula above to find .Please provide the components of if you want the exact angle calculation.