A motor car travels at a constant velocity of 10m for 15 seconds and then accelerates at 0.5m² for 10 seconds. Draw a velocity time graph and calculate the total displacement
To draw the velocity-time graph, we need to plot the velocity of the motor car at different points in time.
Given:
Initial velocity (u) = 10 m/s (constant velocity)
Time (t) = 15 seconds
Acceleration (a) = 0.5 m/s² (accelerating)
Time (t) = 10 seconds
First, let's plot the first 15 seconds when the car is traveling at a constant velocity of 10 m/s.
Since the velocity remains constant, the graph will be a straight line parallel to the time-axis.
The velocity will be constant at 10 m/s from 0 to 15 seconds.
Next, we need to plot the next 10 seconds when the car accelerates at 0.5 m/s².
Since the car is accelerating, the graph will be a straight line at an increasing slope.
Using the equation v = u + at, we can calculate the final velocity (v) at the end of the acceleration phase.
v = u + at
v = 10 + 0.5 * 10
v = 10 + 5
v = 15 m/s
Therefore, the velocity after 10 seconds of acceleration will be 15 m/s.
Now, let's draw the velocity-time graph:
|
15|______________________
| \
| \
10 |______________________ \
| \ \
| \ \
| \ \
5 | \ \
| \ \
| \ \
0 | \ \
|______________________________\______________
0 15 25 (time in seconds)
To calculate the total displacement, we need to find the area under the curve on the velocity-time graph.
For the constant velocity phase (0-15 seconds), the velocity is 10 m/s.
Therefore, the displacement during this period can be calculated using the formula s = v * t, where s is the displacement, v is the velocity, and t is the time.
s = 10 * 15
s = 150 meters
For the acceleration phase (15-25 seconds), the velocity changes from 10 m/s to 15 m/s.
Therefore, the average velocity can be calculated as (10 + 15) / 2 = 12.5 m/s.
Using the same formula s = v * t, we can calculate the displacement during this phase.
s = 12.5 * 10
s = 125 meters
The total displacement is the sum of the displacements in the two phases:
Total displacement = 150 + 125
Total displacement = 275 meters