ANSWER
The required force is
![350N](https://img.qammunity.org/2020/formulas/mathematics/middle-school/yngu1vlnhmj2hc8737xczizpv9ypvi6e1j.png)
Step-by-step explanation
The force needed to accelerate a 70kg runner at
![5ms^(-2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/cqjfhrd5d49271wubdbj8vhrwd0yfo03oi.png)
is the product of the mass of the runner in kilograms and the acceleration in meters per seconds square.
The equation is given by,
![F=ma](https://img.qammunity.org/2020/formulas/physics/middle-school/hoqv0uuwk5hamoxytydy5e8slsjemaiqzz.png)
where
![m = 70kg](https://img.qammunity.org/2020/formulas/mathematics/middle-school/yq440vc72pa8yune2nogpijfb0qxvlol2o.png)
and
![a=5m{s}^(-2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/be2vp0smti5t44k1lvim29tqcvfbgedtqd.png)
This implies that,
![F=70* 5N](https://img.qammunity.org/2020/formulas/mathematics/middle-school/4gsliwn4auet0x84ksgihcxmwlap7fz99c.png)
We multiply to get,
![F=350N](https://img.qammunity.org/2020/formulas/mathematics/middle-school/g9x1lf42ek4h657xfeh5v5agkbtu6ay3pz.png)
Therefore the needed force is 350 Newtons.