A particle has initial velocity of $\left( {\widehat i + \widehat j} \right)\, m/s$ and an acceleration of $\left( {\widehat i + \widehat j} \right)\, m/s^2$. Its speed after $10s$ will be :-

A boy is moving with a constant speed $v$ on a small trolley towards a distant circle as shown in the figure. A point mass is moving on the circle with a constant speed $v$, what is the frequency of change in magnitude of relative velocity of the point mass, as observed by the boy.

A flag is mounted on a car moving due North with velocity of $20 \,\,km/hr$ Strong winds are blowing due East with velocity of $20\,\,km/hr$. The flag will point in direction

A man on a rectilinearly moving cart, facing the direction of motion, throws a ball straight up with respect to himself

In the picture shown, a ball standing from rest rolls down a ramp $AB$, goes along at the horizontal bottom $BC$, and then backs up a smaller ramp $CD$, thereafter rolls on horizontal plane $DE$. Ignore friction and air resistance.Which of the following figure shows variation in speed with time ?

If the position vector of a particle is

$\vec r =  - \cos \,t\hat i + \sin \,t\hat j - 18\,t\hat k$

then what is the magnitude of its acceleration ?