Question

A particle has initial velocity $4i+4jm{s}^{-1}$ and an acceleration $-0.4im{s}^{-2}$, at what time will its speed be $5m{s}^{-1}?$

• A. $2.5s$
• B. $17.5s$
• C. $s$
• D. $8.5s$

Answer 1

The correct option is B $17.5s$

$A,B$

$V_y=4m/s\to \left(1\right)$

$V_x=4-0.4t\to \left(2\right)$

Speed, $V=\sqrt{V_x^2+V_y^2}\to \left(3\right)$

$5=\sqrt{4^2+V_x^2}$

$\Rightarrow V_x=\pm 3\to \left(4\right)$

$\left(4\right)$ in $\left(2\right)$ $\Rightarrow 3=4-0.4t$

$\Rightarrow t=2.5s$

also, $-3=4-0.4t$

$\Rightarrow t=17.5s$