Generated on Mar 21, 2025, 12:41:15 PMgpt-4o-mini
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:
We can express (t) in terms of (a):
From (v_f = v_i + at), we get (t = \frac{v_f - v_i}{a} = \frac{30 - 10}{a} = \frac{20}{a}).
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.