The position of a particle varies with time as vec r = (5t^2i - 5tj) m .

Question

The position of a particle varies with time as \(\vec r = (5t^2\hat i - 5t\hat j)\ m\ .\) The magnitude and direction of velocity at \(t = \frac{1}{2}s\) is

(1) \(5\sqrt{2} \ m / s,\ -45^\circ \ with + X\ axis\)

(2) \(5\ m/s, \ –45° \ with\ +\ X \ axis\)

(3) \(5 \sqrt{2}\ m/s, \ –45°\ with\ +\ Y\ axis\)

(4) \(5 \ m/s,\ +45°\ with\ +\ Y \ axis\)

Answer 1

Correct option is : (1) \(5\sqrt{2} \ m / s,\ -45^\circ \ with + X\ axis\) 

\(\vec r = 5t^2\hat i - 5t\hat j\)

\(\vec v = \frac{d \vec r}{dt} = 10t\hat i -5\hat j\)

\(\vec v = \left( t = \frac{1}{2}\ s\right) =10 \left( \frac{1}{2}\right) \hat i- 5\hat j\)

\( =5 \hat i - 5 \hat j\)

Magnitude = \(\sqrt{(5)^2 + (-5)^2} = 5\sqrt{2}\ m / s\)