Question

Matthew is cycling of a Speed of 4 meters per second . When he starts down the hill the bike wheb he starts down a hill , the bike accelerates at a rate of 0.4 m/s squared the vertical distance from the top of the hill to the bottom of the hill is 25 m is the equation d(t)=v0t+1/2 at^2 two find how long it will take mathew to ridedown the hill

Answer 1

Answer:

Mathew will take 5 seconds to ride down the hill.

Step-by-step explanation:

Given equation is:    $d(t)= v_{0}t +\frac{1}{2}at^2$

Matthew is cycling of a speed of 4 meters/second. So,  $v_{0}= 4 m/s$

When he starts down a hill, the bike accelerates at a rate of 0.4 m/s². So,  $a= 0.4 m/s^2$

The vertical distance from the top of the hill to the bottom of the hill is 25 meters. So, $d(t)= 25$ meters.

Plugging the values into the above equation, we will get......

$25= 4t+\frac{1}{2}(0.4)t^2\\ \\ 25= 4t+0.2t^2\\ \\ 0.2t^2+4t-25=0$

Using quadratic formula, we will get.......

$t= \frac{-4\pm \sqrt{4^2-4(0.2)(-25)}}{2(0.2)}\\ \\ t=\frac{-4\pm \sqrt{16+20}}{0.4}\\ \\ t=\frac{-4\pm \sqrt{36}}{0.4}=\frac{-4\pm 6}{0.4}\\ \\ t=\frac{-4+6}{0.4}=\frac{2}{0.4}=5\\ \\or\\ \\ t=\frac{-4-6}{0.4}=\frac{-10}{0.4}=-25$

(Negative value is ignored as the time can't be negative)

So, Mathew will take 5 seconds to ride down the hill.