Question

Need help with questions a and b please try to explain in the simple definition I am in year 9

Answer 1

Answer:

a) 130 m

b) -1.25 m/s²

Explanation:

Part a)

The total distance traveled on the cycle is equal to the area under the velocity-time graph.

This is the area of a trapezoid where the bases are 20 and 6 and the height is 10.

Then, the area is equal to:

$\begin{gathered} \text{Area = }\frac{base_1+\text{base}_2}{2}\times\text{height} \\ \text{Area = }\frac{20+6}{2}\times10 \\ \text{Area}=\frac{26}{2}\times10 \\ \text{Area = 13x10 = 130} \end{gathered}$

Therefore, the total distance traveled on the cycle is 130 meters.

Part b)

The acceleration in the last 8 seconds is equal to the slope of the line in the last 8 seconds.

The slope can be calculated using two points of the line (t1, v1) and (t2, v2) as follows

$\text{slope}=\frac{v_2-v_1}{t_2-t_1}$

So, replacing (t1, v1) by (12, 10) and (t2, v2) by (20, 0), we get:

$\text{slope}=\text{ }\frac{0-10}{20-12}=\frac{-10}{8}=-1.25$

Therefore, the acceleration in the last 8 seconds is -1.25 m/s²