a motor travels at a constant velocity of 10 m/s for 15 seconds and then accelerates at 0.5 m/s ² for 10 seconds .
calculate the velocity of the motor car
make a neat labelled sketch of the velocity of the time graph for the motion
determine the total displacement of
the graph.
the average velocity of the motor car
To calculate the velocity of the motor car, we can use the equation:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
For the first part of the motion, where the motor car travels at a constant velocity of 10 m/s for 15 seconds, the initial velocity (u) is 10 m/s, acceleration (a) is 0 m/s², and time (t) is 15 seconds. Plugging these values into the equation, we get:
v = 10 + 0 * 15
v = 10 m/s
So, the velocity of the motor car during the first part is 10 m/s.
For the second part of the motion, where the motor car accelerates at 0.5 m/s² for 10 seconds, the initial velocity (u) is 10 m/s, acceleration (a) is 0.5 m/s², and time (t) is 10 seconds. Plugging these values into the equation, we get:
v = 10 + 0.5 * 10
v = 15 m/s
So, the velocity of the motor car during the second part is 15 m/s.
Now, let's make a neat labeled sketch of the velocity-time graph for this motion:
|
Velocity| 15
(m/s) |
| _________
| |
| ___________ __
| / 10 |__________________________
|/___________________________________________ Time (s)
For the total displacement of the graph, we can calculate it by dividing the motion into two parts:
For the first part, the motor car is traveling at a constant velocity of 10 m/s for 15 seconds. The displacement during this part is given by:
displacement = velocity * time
displacement = 10 * 15
displacement = 150 meters
For the second part, the motor car is accelerating at 0.5 m/s² for 10 seconds. The displacement during this part is given by:
displacement = initial velocity * time + 0.5 * acceleration * time²
displacement = 10 * 10 + 0.5 * 0.5 * 10²
displacement = 100 + 0.5 * 0.5 * 100
displacement = 100 + 0.25 * 100
displacement = 100 + 25
displacement = 125 meters
Therefore, the total displacement of the graph is 150 + 125 = 275 meters.
To calculate the average velocity of the motor car, we can use the formula:
average velocity = total displacement / total time
The total time for the motion is the sum of the times for each part, which is 15 + 10 = 25 seconds. Plugging in the total displacement of 275 meters and the total time of 25 seconds into the formula, we get:
average velocity = 275 / 25
average velocity = 11 m/s
Therefore, the average velocity of the motor car is 11 m/s.