Question

two particles start moving from the same point along the same straight line. the first moves with constant velocity v and the second with constant acceleration a. during the time that elapses before the second catches the first the greatest distance between the particles is

Answer 1

Difference between particle 1 and 2 at time t is given by

d = ut - \frac{1}{2} a {t}^{2}d=ut−

2

1

at

2

for maxima let it derivative = 0

\begin{gathered}u - 2at = 0 \\ t = \frac{u}{2a} \end{gathered}

u−2at=0

t=

2a

u

and distance will be

d = \frac{ {u}^{2} }{2a} - \frac{a. {u}^{2} }{8 {a}^{2} } = \frac{3 {u}^{2} }{8a}d=

2a

u

2

−

8a

2

a.u

2

=

8a

3u

2

Difference between particle 1 and 2 at time t is given by

d = ut - \frac{1}{2} a {t}^{2}d=ut−

2

1

at

2

for maxima let it derivative = 0

\begin{gathered}u - 2at = 0 \\ t = \frac{u}{2a} \end{gathered}

u−2at=0

t=

2a

u

and distance will be

d = \frac{ {u}^{2} }{2a} - \frac{a. {u}^{2} }{8 {a}^{2} } = \frac{3 {u}^{2} }{8a}d=

2a

u

2

−

8a

2

a.u

2

=

8a

3u

2.