Answer:
a) The distance travelled on the cycle in the first 14 seconds is 96 meters.
b) The acceleration in the first 4 seconds is 2 meters per square second.
Step-by-step explanation:
a) The distance travelled by the cycle is equal to the area below the curve, which is the sum of the first triangle and the rectangle:
[tex]\Delta x = \frac{1}{2}\cdot \left(8\,\frac{m}{s} \right) \cdot (4\,s-0\,s)+\left(8\,\frac{m}{s}\right)\cdot (14\,s-4\,s)[/tex]
[tex]\Delta x = 16\,m +80\,m[/tex]
[tex]\Delta x = 96\,m[/tex]
The distance travelled on the cycle in the first 14 seconds is 96 meters.
b) The acceleration is represented by the slope of the line, which is determined by definition of secant line:
[tex]a = \frac{v(4\,s)-v(0\,s)}{4\,s-0\,s}[/tex] (1)
[tex]a = \frac{8\,\frac{m}{s}-0\,\frac{m}{s}}{4\,s-0\,s}[/tex]
[tex]a =2\,\frac{m}{s^{2}}[/tex]
The acceleration in the first 4 seconds is 2 meters per square second.
