The greatest acceleration on the graph is 4 m/s² .
"Acceleration" means how fast velocity is changing.
Changing velocity means changing speed OR direction.
This graph doesn't tell us anything about the direction of motion, so we can only work with speed.
The "greatest" acceleration means the biggest change of speed in the shortest time.
Your picture of the graph is pretty fuzzy, and I'm not sure I can actually read everything correctly.
The y-axis looks like it's velocity, and I THINK the numbers are 0, 20, 40, and 60, in meters per second.
The x-axis looks like time, and I THINK it's marked 0, 10, 20, 30, 40, 50, 60, 70, and 80, in seconds.
Now, each straight piece on the graph shows a change of velocity and a change of time. So the SLOPE of each piece is the acceleration of that piece.
==> On the first piece, from 0 to A, the velocity changes from 0 to 20 m/s, and the time changes from 0 to 20 sec. The slope of that piece is (20 m/s) / (20 sec), so the acceleration is 1 m/s² .
==> On the level piece from A to B, the velocity is 20 m/s. It doesn't change, from 20 to 30 sec. It has no slope, so the acceleration is zero.
==> On the piece from B to C, the velocity rises (60 - 20) = 40 m/s, and the time changes (40 - 30) = 10 sec. The slope is (40 m/s) / (10 sec), so the cceleration on that piece is 4 m/s² .
==> Finally, on the last piece, from C to D, the velocity DROPS from 60 to 0 m/s, during the time from 40 to 80 sec. The change in velocity is -60 m/s, and the change in time is 40 sec. So the slope of the piece, and the acceleration, is (-60 m/s) / (40 sec) = -1.5 m/s² .
The greatest acceleration shown on the graph happens along the line segment from B to C, from 30 to 40 seconds. During that time, the velocity changes from 20 to 60 m/s. That's an acceleration of 4 m/s² .
