Answer:
(a) 34 m/s
(b) k = 42.5
Step-by-step explanation:
Part (a)
[tex]\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]
Given:
- Distance = 1.7 km = 1700 m
- Time = 50 s
Substitute the values into the formula to find the average speed :
[tex]\implies \sf Speed = \dfrac{1700}{50}=34\;m/s[/tex]
Part (b)
The area under a speed-time graph represents the distance traveled.
Separate the area under the graph into a rectangle and a triangle, where:
- The area of the rectangle represents the distance traveled in the first 30 seconds of the journey.
- The area of the triangle represents the distance traveled in the last 20 seconds of the journey.
[tex]\boxed{\textsf{Area of a rectangle $=$ width $\times$ length}}[/tex]
Therefore, the distance traveled in the first 30 seconds of the journey is:
[tex]\implies \sf 30k[/tex]
[tex]\boxed{\textsf{Area of a triangle $=\dfrac{1}{2} \times$ base $\times$ height}}[/tex]
Therefore, the distance traveled in the last 20 seconds of the journey is:
[tex]\implies \sf \dfrac{1}{2}(20)k[/tex]
Therefore:
[tex]\implies \sf 30k+\dfrac{1}{2}(20)k=1700[/tex]
[tex]\implies \sf 30k+10k=1700[/tex]
[tex]\implies \sf 40k=1700[/tex]
[tex]\implies \sf \dfrac{40k}{40}=\dfrac{1700}{40}[/tex]
[tex]\implies \sf k=42.5[/tex]
