(Solved): Suppose the position vector for a particle is given as a function of time by \( \vec{r}(t)=x(t) \h ...

Suppose the position vector for a particle is given as a function of time by \( \vec{r}(t)=x(t) \hat{i}+y(t) \mathbf{j} \), with \( x(t)=a t+b \) and \( y(t)=c t^{2}+d \), where \( a=1 \) and \( d=1.08 \mathrm{~m} \). (a) Calculate the average velocity during the time interval from \( t=1.80 \mathrm{~s} \) to \( t=3.75 \mathrm{~s} \). \( \vec{v}= \) \[ x^{m / s} \] (b) Determine the velocity at \( t=1.80 \mathrm{~s} \). \( \vec{v}= \) \( m / s \) Detarmine the speed at \( t=1.800 \). on vector for a particle is given as a function of time by \( \vec{r}(t)=x(t) \vec{i}+v(t) j \), with \( x(c)=a t-b \) and \( y(t)=c t^{2}+d_{f} \) where a \( =2.50 m / s, b=1,50 m, c=0,124 m / s^{2} \). ate the average veiocity during the time interval from \( t=1.80 \) i to \( t \) w \( 3.755 \). \[ \mathrm{m} / \mathrm{s} \] Whine the veloeity at \( t=-1.80 \) s. \[ \mathrm{m} / \mathrm{s}= \] the speed at \( t=1.80 \) He mis