how far did the object travel by the end of eight seconds, according to the graph above?

24 cm

Explanation:

You know the equation for speed: v = Δd/Δt.

This is easy to use to find the distance travelled for the second half of the graph (4-8s) where the speed is constant:

4 = Δd / 4

Δd = 16 cm

For the first part (0-4s), the speed is changing. Since it is changing at a constant rate (i.e. the acceleration is constant), you can find the average speed (lowest speed + highest speed / 2) and use that in the equation above instead. In this case, the average speed is (0 + 4) / 2 = 2 cm/s. Plugging that into the equation above:

2 = Δd / 4

Δd = 8 cm

The total distance traveled is 16cm + 8cm = 24cm.

the distance traveled in the 8 seconds is equal to 22cm

Explanation: Here we have a graph of speed vs time.

between the seconds 0 and 4, the speed grows linearly with the time as:

v(t) = t*1cm/s^2

and after the second 4s, the speed is constant:

v(t) = 4cm/s

so we can integrate both parts by separated:

1)

the integral of t*1cm/s^2 over the time is equal to:

(t^2)/2 *1cm/s^2 + c

where c is a constant of integration.

If we calculate this between t = 4s and t = 0s, we got:

d1 = (4^2)/2 cm/s^2 + c - (0^2)/2 cm/s^2 - c = 8cm

so in the first 4 seconds, the object traveled 8 cm-

2)

now the integration is easier, v = 4cm/s, then in 4 seconds, the object moves 4cm four times; then we got:

d2 = 4cm/s*4s = 16cm

then the total distance that the object moves in the 8 seconds is:

d1 + d2 = 8cm + 16cm = 22cm