A car starts from rest and attains a velocity of 40 metres per second in 20 seconds. it maintains this velocity for 30 seconds and then comes to rest in 25 seconds.
1. sketch the velocity time graph for the motion.
2. Calculate the acceleration of the body.
3. Calculate the total distance covered by the body.
Please show working.
http://www.jiskha.com/display.cgi?id=1478031138
TIME GRAPH
Show workings
1. To sketch the velocity-time graph, we need to first identify the key points of the motion.
From the information provided, we can break down the motion into three intervals:
Interval 1: Car starts from rest and attains a velocity of 40 meters per second in 20 seconds.
Interval 2: Car maintains this velocity (40 m/s) for 30 seconds.
Interval 3: Car comes to rest in 25 seconds.
Now, let's plot the key points on the graph:
- At the start, the velocity is zero.
- At the end of Interval 1 (20 seconds), the velocity is 40 m/s.
- From the end of Interval 1 to the start of Interval 3 (50 seconds), the velocity remains constant at 40 m/s.
- At the end, the velocity is zero again.
So, the velocity-time graph would look like this:
^
|
| .
| .
| .
| .
| .
| .
|-------|---------|--------------|------
0 20 sec 50 sec 80 sec
The x-axis represents time (in seconds), and the y-axis represents velocity (in meters per second).
2. To calculate the acceleration, we can use the formula:
acceleration = change in velocity / time
We know that the car started from rest (velocity = 0 m/s) and attained a velocity of 40 m/s in 20 seconds during Interval 1. So,
acceleration = (final velocity - initial velocity) / time
= (40 m/s - 0 m/s) / 20 s
= 40 m/s / 20 s
= 2 m/s²
Therefore, the acceleration of the car is 2 m/s².
3. To calculate the total distance covered by the body, we need to consider each interval separately.
Interval 1: To calculate the distance covered during Interval 1, we can use the formula:
distance = initial velocity * time + (1/2) * acceleration * time²
Given:
initial velocity = 0 m/s
final velocity = 40 m/s
time = 20 s
distance = 0 m/s * 20 s + (1/2) * 2 m/s² * 20 s²
= (1/2) * 2 m/s² * 400 s²
= 400 m
Interval 2: The car maintains the same velocity (40 m/s) for 30 seconds. Therefore, the distance covered is:
distance = velocity * time
= 40 m/s * 30 s
= 1200 m
Interval 3: The car comes to rest in 25 seconds, so the distance covered is:
distance = (1/2) * acceleration * time²
= (1/2) * (-2 m/s²) * (25 s)² (Note: Negative acceleration is used because the car is decelerating to come to rest)
= -250 m
Now, to calculate the total distance, we sum up the distances covered in each interval:
total distance = distance in Interval 1 + distance in Interval 2 + distance in Interval 3
= 400 m + 1200 m + (-250 m)
= 1350 m
Therefore, the total distance covered by the car is 1350 meters.