A car travels with uniform velocity of 30m/s for 5s and then comes to rest in the next 10s with uniform deceleration . Draw a velocity time graph of the motion, from the graph, find
A) the deceleration
B)the total distance covered
C) acceleration
D) average speed................
My response
To draw the velocity-time graph for the given motion, we will consider the different stages of the car's motion.
Stage 1: Constant Velocity
The car travels with a uniform velocity of 30 m/s for 5 seconds. Therefore, the velocity remains constant at 30 m/s during this period.
Stage 2: Deceleration
The car then comes to rest (velocity becomes zero) in the next 10 seconds with uniform deceleration.
Based on this information, here's the step-by-step explanation:
1. On the vertical axis, mark the velocity values ranging from 0 m/s to 30 m/s.
2. On the horizontal axis, mark the time values ranging from 0 seconds to 15 seconds.
3. During the first 5 seconds, draw a horizontal line parallel to the time axis at 30 m/s to represent the constant velocity.
4. From the end of the first 5 seconds, draw a straight line with a negative slope (decreasing velocity) until it intersects the x-axis at 15 seconds (10 seconds of deceleration).
The velocity-time graph will look like this:
|\
30 ----| \
| \
| \
| \
| \
| \
|-------\
5 10 15 (time in seconds)
Now let's find the answers to the questions:
A) The Deceleration:
The deceleration can be determined from the slope of the line representing the deceleration. In this case, the slope is constant, indicating uniform deceleration. The slope can be calculated using the formula:
Deceleration = Change in velocity / Time taken
The change in velocity is 30 m/s (from 30 m/s to 0 m/s), and the time taken is 10 seconds.
Therefore, the deceleration = 30 m/s / 10 s = 3 m/s^2.
B) The Total Distance Covered:
To find the total distance covered, we need to calculate the area under the velocity-time graph. Since the motion consists of two parts (constant velocity and deceleration), we need to calculate the area of each part separately and then add them.
1. Area of the rectangle representing the constant velocity:
Length of the rectangle = 5 seconds
Width of the rectangle = 30 m/s
Area = Length x Width = 5 s x 30 m/s = 150 m
2. Area of the triangle representing deceleration:
Base of the triangle = 10 seconds
Height of the triangle = 30 m/s
Area = 1/2 x Base x Height = 1/2 x 10 s x 30 m/s = 150 m
Total distance covered = Area of constant velocity + Area of deceleration
= 150 m + 150 m = 300 m
C) The Acceleration:
During the constant velocity stage, the acceleration is zero since the velocity remains constant.
D) The Average Speed:
To calculate the average speed, we need to divide the total distance covered by the total time taken. The total time taken is 15 seconds (5 seconds of constant velocity + 10 seconds of deceleration).
Average Speed = Total Distance / Total Time = 300 m / 15 s = 20 m/s
To draw the velocity-time graph and find the required values, we can follow these steps:
Step 1: Draw the axes for the graph. The x-axis represents time (in seconds), and the y-axis represents velocity (in meters per second).
Step 2: Divide the graph into two parts: the first part represents the car's motion with uniform velocity, and the second part shows the car coming to rest with uniform deceleration.
Step 3: For the first part of the graph (uniform velocity), draw a straight line parallel to the x-axis at a height of 30 m/s for a duration of 5 seconds (from 0s to 5s).
Step 4: For the second part of the graph (uniform deceleration), draw a straight line with a negative slope from the end point of the first part (at 5s) to the x-axis at a duration of 10 seconds (from 5s to 15s).
Now, let's find the required values based on the graph:
A) Deceleration:
The deceleration can be found by calculating the slope of the velocity-time graph during the deceleration period. In this case, the negative slope represents deceleration.
To calculate the deceleration:
deceleration = change in velocity / change in time
From the graph, we see that the change in velocity is -30 m/s (the car goes from 30 m/s to 0 m/s), and the change in time is 10 seconds. Therefore,
deceleration = -30 m/s / 10 s = -3 m/s²
B) Total distance covered:
To find the total distance covered, we need to calculate the area under the velocity-time graph. Since the graph consists of two parts, we will calculate the area individually for each part and then add them together.
For the first part (uniform velocity):
Area of a rectangle = base * height = 5 s * 30 m/s = 150 m
For the second part (uniform deceleration):
Area of a triangle = 0.5 * base * height = 10 s * (30 m/s - 0 m/s) * 0.5 = 150 m
Therefore, the total distance covered by the car is:
Total distance = 150 m + 150 m = 300 m
C) Acceleration:
Since the car has only been stated to have a uniform deceleration (negative acceleration), we don't have any information or need to calculate the acceleration.
D) Average speed:
The average speed can be found by dividing the total distance traveled by the total time taken.
Total time taken = time for uniform velocity + time for uniform deceleration = 5 s + 10 s = 15 s
Average speed = Total distance / Total time taken = 300 m / 15 s = 20 m/s
So, the answers to the questions are:
A) The deceleration is -3 m/s².
B) The total distance covered is 300 meters.
C) There is no acceleration given.
D) The average speed is 20 m/s.