A car starting from rest & moves for 20 seconds its velocity reach 5 m/s & moves at this velocity for 30 seconds.its velocity increases to 10 m/s over 10 seconds.it moves at this velocity for 40 seconds & then slows down to come to rest after further 60 secnds.draw velocity-time graph for the car's journy
stage 1: a = 4 m/s^2
stage 2: a = 0
stage 3: a = 1/2 m/s^2
stage 4: a=0
stage 5: a = -1/6 m/s^2
For each stage, the acceleration is the slope of the graph.
It's not clear
stage 1
v = v initial + a t
v = 0 + a t
5 = 20 a
a = (1/4) m/s^2
so v = 0.25 t for the first 20 seconds, t = 0 to t = 20
stage 2
v = constant 5 m/s from t = 20 to t = 50
etc
To draw the velocity-time graph for the car's journey, we can break down the journey into different stages and plot the corresponding velocities at each stage.
Let's divide the journey into four stages:
1. Stage 1: From rest to reaching a velocity of 5 m/s (20 seconds)
2. Stage 2: Moving with a constant velocity of 5 m/s (30 seconds)
3. Stage 3: Increasing velocity from 5 m/s to 10 m/s (10 seconds)
4. Stage 4: Moving with a constant velocity of 10 m/s (40 seconds) until coming to rest (60 seconds)
Now, let's plot the velocity-time graph based on the information given:
Start by setting up the axes.
- The x-axis represents time (in seconds).
- The y-axis represents velocity (in m/s).
Stage 1:
From rest, the car's velocity increases linearly to 5 m/s over 20 seconds. This is represented by a straight line segment with a positive slope connecting the points (0, 0) and (20, 5).
Stage 2:
The car maintains a constant velocity of 5 m/s for 30 seconds. This is represented by a horizontal line segment at y = 5, from (20, 5) to (50, 5).
Stage 3:
The car's velocity increases from 5 m/s to 10 m/s over 10 seconds. This is represented by a straight line segment with a positive slope connecting the points (50, 5) and (60, 10).
Stage 4:
The car maintains a constant velocity of 10 m/s for 40 seconds until it comes to rest after an additional 60 seconds. This is represented by a horizontal line segment at y = 10, from (60, 10) to (100, 10). Afterward, the velocity drops to zero at t = 100 seconds.
Thus, the velocity-time graph for the car's journey would look like this:
|
10 |- - - - - - - - - - - - - - - - - -|
| |_____________________
| ______________
| _____________| |_____________________
5 |- -| |
| |
| |
| |
0 |- - - - - - - - - - - - - - - - - - - - - - - - - -
0 20 50 60 100 -> Time (seconds)
The graph shows the car's velocity changing over time during its entire journey.