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 .

Question

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

Answer 1

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.