54.6k views
1 vote
Please, i need help for part b, my hw is due tomorrow, please help, any help will be appreciated,

The graph shows the speed of a vehicle during the final 50 seconds of a journey.
At the start of the 50 seconds the speed is k metres per second.
The distance travelled during the 50 seconds is 1.7 kilometres.


b) Work out the value of k.

Please, i need help for part b, my hw is due tomorrow, please help, any help will-example-1
User Michi
by
8.2k points

2 Answers

2 votes

Answer:

k is 42.5 m/s

Explanation:

we need to calculate the distance that was covered when the speed was k m/s

from the graph k m/s was travelled for 30 seconds

the entire time for the journey was 50 seconds

the entire journey was 1700 m

Alternatively the area under the graph represents the total distance covered.

Area of a trapezium = 1/2(a+b)h

= 1/2( 30+50)k

= 40k

we equate it to the total distance covered

1700 = 40k.

k = 42.5

Thus k is 42.5 m/s

User Luca Mastrostefano
by
7.6k points
2 votes

Answer:

(a) 34 m/s

(b) k = 42.5

Explanation:

Part (a)


\boxed{\sf Speed=(Distance)/(Time)}

Given:

  • Distance = 1.7 km = 1700 m
  • Time = 50 s

Substitute the values into the formula to find the average speed :


\implies \sf Speed = (1700)/(50)=34\;m/s

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.


\boxed{\textsf{Area of a rectangle $=$ width $*$ length}}

Therefore, the distance traveled in the first 30 seconds of the journey is:


\implies \sf 30k


\boxed{\textsf{Area of a triangle $=(1)/(2) *$ base $*$ height}}

Therefore, the distance traveled in the last 20 seconds of the journey is:


\implies \sf (1)/(2)(20)k

Therefore:


\implies \sf 30k+(1)/(2)(20)k=1700


\implies \sf 30k+10k=1700


\implies \sf 40k=1700


\implies \sf (40k)/(40)=(1700)/(40)


\implies \sf k=42.5

User Kahowell
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories