To calculate the acceleration, we can use the formula:

[ a = \frac{v_f - v_i}{t} ]

However, we first need to find the time (t) it takes to accelerate. We can use the equation of motion:

[ d = v_i t + \frac{1}{2} a t^2 ]

We also know:

1. Initial velocity ((v_i)) = 10 m/s
2. Final velocity ((v_f)) = 30 m/s
3. Distance ((d)) = 100 m

We can express (t) in terms of (a):

1. From (v_f = v_i + at), we get (t = \frac{v_f - v_i}{a} = \frac{30 - 10}{a} = \frac{20}{a}).

2. Substitute (t) into the distance equation:

[ 100 = 10 \left(\frac{20}{a}\right) + \frac{1}{2} a \left(\frac{20}{a}\right)^2 ]

This simplifies to:

[ 100 = \frac{200}{a} + \frac{1}{2} a \cdot \frac{400}{a^2} ]

[ 100 = \frac{200}{a} + \frac{200}{a} ]

[ 100 = \frac{400}{a} ]

Now, solving for (a):

[ a = \frac{400}{100} = 4 , \text{m/s}^2 ]

The acceleration is (4 , \text{m/s}^2).

On a distance-time graph, this acceleration would be represented by a curve that becomes steeper over time, indicating that the object is covering more distance in each successive time interval as its speed increases. The graph would start at a point corresponding to 10 m/s and curve upwards to reflect the increasing distance covered as the speed approaches 30 m/s.