Question

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

Answer 1

a) 130 m

b) -1.25 m/s²

Step-by-step 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}*\text{height} \\ \text{Area = }(20+6)/(2)*10 \\ \text{Area}=(26)/(2)*10 \\ \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}=(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{ }(0-10)/(20-12)=(-10)/(8)=-1.25`

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