Question

A speedboat moving at 30.0 m/s approaches a ship 100 m ahead. The pilot slows the boat with a constant acceleration of -3.50 m/s2. How long does it take the boat to reach the ship?

Answer 1

Using $3^{rd}$  kinematics equation-

$s=ut+0.5at^{2}$

here,

s is the displacement

u is the initial velocity

a is the acceleration

t is time

Given : s = 100m , a = -3.50m$s^{-2}$ , u = 30m$s^{-1}$

Putting the values-

$100=30t-1.75t^2$

$175t^2-3000t+10000=0$

$(t-4.531)(t-12.612)=0$

Here t = 12.612s is not possible. Hence, time taken by boat to reach the ship is 4.531s