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

It’ll only take Mathew 5 seconds to ride his bike down the hill.

Explanation:

Answer 2

Mathew will take 5 seconds to ride down the hill.

Explanation:

Given equation is:
`d(t)= v_(0)t +(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+(1)/(2)(0.4)t^2\\ \\ 25= 4t+0.2t^2\\ \\ 0.2t^2+4t-25=0`

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

`t= (-4\pm √(4^2-4(0.2)(-25)))/(2(0.2))\\ \\ t=(-4\pm √(16+20))/(0.4)\\ \\ t=(-4\pm √(36))/(0.4)=(-4\pm 6)/(0.4)\\ \\ t=(-4+6)/(0.4)=(2)/(0.4)=5\\ \\or\\ \\ t=(-4-6)/(0.4)=(-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.