velocity 16 20 24 24 24 21 18,time 0 10 20 40 60 70 80. show how the velocity of a car changed during part of a journey along a main road. (a)draw a valocity -time grapy for the journey.(b)write brief description of the journey.(c)the car's speed changed during two parts of the journey. calculate its acceleration at these time.
To create a velocity-time graph for the given journey, plot the velocity values (in km/h) on the y-axis and the corresponding time values (in minutes) on the x-axis.
(a) Velocity-Time Graph:
Now, let's plot the data points on a graph based on the given values.
The given data points are:
Velocity (km/h): 16, 20, 24, 24, 24, 21, 18
Time (minutes): 0, 10, 20, 40, 60, 70, 80
Plot the points (0, 16), (10, 20), (20, 24), (40, 24), (60, 24), (70, 21), (80, 18) on the graph.
^
Velocity (km/h) |
26 ┤
24 ├────────────────────────
22 | ┼
20 ┤ │
18 ←───┼───┼───┼───┼───┼───┼─────────────────────→
0 10 20 30 40 50 60 70 80
Time (minutes)
(b) Brief Description of the Journey:
Based on the graph, we can see that the car's velocity starts at 16 km/h and gradually increases to 24 km/h within the first 20 minutes. It maintains a constant speed of 24 km/h for 40 minutes until it starts to decelerate slightly at 60 minutes with a velocity of 21 km/h. The car's velocity further reduces to 18 km/h at 80 minutes.
(c) Calculation of Acceleration:
Acceleration represents the rate of change of velocity with respect to time. To calculate acceleration, we can use the formula:
Acceleration (a) = (Final Velocity - Initial Velocity) / Time
From the graph, we can determine the times when the car's speed changed: at 20 minutes and 60 minutes.
At 20 minutes:
Initial Velocity (u) = 24 km/h (starting at 20 minutes)
Final Velocity (v) = 24 km/h (unchanged at 40 minutes)
Time (t) = 20 minutes
Acceleration (a) = (v - u) / t
= (24 - 24) / 20
= 0 / 20
= 0 km/h²
At 60 minutes:
Initial Velocity (u) = 24 km/h (starting at 40 minutes)
Final Velocity (v) = 21 km/h (at 70 minutes)
Time (t) = 20 minutes
Acceleration (a) = (v - u) / t
= (21 - 24) / 20
= -3 / 20
= -0.15 km/h²
The car's acceleration at these times is 0 km/h² (constant speed) at 20 minutes and -0.15 km/h² (deceleration) at 60 minutes.