Now I can see the velocity-time graph more clearly. The x-axis represents time in hours, ranging from 0 to 1.1, and the y-axis represents velocity in km/h, ranging from 0 to 80.0. The graph shows a piecewise linear function with several segments: it starts at (0,0), rises to (0.2,60), stays constant at 60 until (0.4,60), then decreases to (0.7,0), remains at 0 until (0.8,0), then increases again to (1.0,40), and finally stays constant at 40 until (1.1,40).
Let me now answer each question based on this graph:
a. At what time was the car stopped?
The car is stopped when velocity = 0. Looking at the graph, velocity is 0 at t=0 and from t=0.7 to t=0.8. So the car was stopped at t=0 and between t=0.7 and t=0.8 hours.
b. At what time did the car have the greatest velocity?
The greatest velocity is 60 km/h, which occurs from t=0.2 to t=0.4 hours.
c. What was its greatest velocity?
As seen from the graph, the greatest velocity reached is 60 km/h.
d. At what time(s) was the car accelerating?
Acceleration is the rate of change of velocity. The car is accelerating when the velocity is increasing (positive slope). This occurs from t=0 to t=0.2 hours and from t=0.8 to t=1.0 hours.
e. How fast was the car going at 1.0 h?
At t=1.0 hours, the velocity is 40 km/h according to the graph.
f. What was the acceleration at 0.9 h?
To find acceleration at 0.9 h, I need to calculate the slope of the line segment at that point. From t=0.8 to t=1.0, the velocity increases from 0 to 40 km/h. The slope (acceleration) = (change in velocity)/(change in time) = (40-0)/(1.0-0.8) = 40/0.2 = 200 km/h².
I've answered all the questions based on the velocity-time graph. Let me summarize my findings.
The solution to the worksheet problems is as follows:
a. The car was stopped at t=0 and between t=0.7 and t=0.8 hours.
b. The car had its greatest velocity from t=0.2 to t=0.4 hours.
c. The greatest velocity was 60 km/h.
d. The car was accelerating from t=0 to t=0.2 hours and from t=0.8 to t=1.0 hours.
e. At 1.0 hour, the car was going 40 km/h.
f. The acceleration at 0.9 hours was 200 km/h².
Parent Tip: Review the logic above to help your child master the concept of velocity time graph worksheet answers.
