A car accelerates from rest at 5 m/s2 for 5 seconds. It moves with a constant velocity for some time, and then decelerates at 5 m/s2 to come to rest. The entire journey takes 25 seconds. On a separate sheet of paper, plot the velocity-time graph of the motion. Describe the shape of the graph here.
To plot the velocity-time graph for the given scenario, we need to break it down into three distinct phases: acceleration, constant velocity, and deceleration.
1. Acceleration phase: The car accelerates from rest at a rate of 5 m/s^2 for 5 seconds. We know that the initial velocity is 0 m/s, the acceleration is 5 m/s^2, and the time is 5 seconds. Using the equation v = u + at, where v represents final velocity, u represents initial velocity, a represents acceleration, and t represents time, we can calculate the final velocity as follows:
v = 0 + (5 * 5)
v = 0 + 25
v = 25 m/s
2. Constant velocity phase: The car moves with a constant velocity. We know that the velocity remains at 25 m/s for a certain amount of time. Let's say this time is represented by t2.
3. Deceleration phase: The car decelerates at 5 m/s^2 to come to rest. We know that the initial velocity is 25 m/s, the acceleration is -5 m/s^2 (negative because it's deceleration), and the final velocity is 0 m/s. Using the equation v = u + at, we can calculate the time taken for the car to come to rest as follows:
0 = 25 + (-5 * t)
-25 = -5t
t = 5 seconds
Now, let's plot the velocity-time graph:
Time (s) Velocity (m/s)
0 0
5 25
t2 25
25 0
The graph would have a straight line with an upward slope from 0 to 25 at 5 seconds, followed by a flat line at 25 m/s until time t2, and finally a straight line with a downward slope from 25 to 0 m/s at 25 seconds.
To plot the velocity-time graph and describe its shape, we need to analyze the given information and break the journey into different stages. Let's go step by step:
1. Stage 1: Acceleration from rest at 5 m/s² for 5 seconds.
During this stage, the velocity of the car increases linearly at a constant rate of 5 m/s² for 5 seconds. To find the final velocity after this stage, we can use the formula:
V = u + at
Where:
- V is the final velocity
- u is the initial velocity (which is 0, as the car starts from rest)
- a is the acceleration (which is 5 m/s²)
- t is the time duration (which is 5 seconds)
So, V = 0 + (5 m/s²)(5 s) = 25 m/s
2. Stage 2: Constant velocity.
During this stage, the car maintains a constant velocity. As the graph is a velocity-time graph, this stage is represented by a horizontal line at the height of the velocity achieved in stage 1, which is 25 m/s.
3. Stage 3: Deceleration at 5 m/s² to rest.
During this stage, the car decelerates with an acceleration of -5 m/s² (negative sign because it's in the opposite direction of the initial acceleration) until it comes to rest. We can use the same formula as before to find the time it takes to decelerate to rest:
V = u + at
Where:
- V is the final velocity (which is 0)
- u is the initial velocity (which is 25 m/s, the velocity achieved in stage 1)
- a is the acceleration (which is -5 m/s²)
- t is the time duration (which we need to find)
0 = 25 m/s + (-5 m/s²)(t)
-25 m/s = -5 m/s²(t)
t = 5 seconds
Therefore, it takes 5 seconds to decelerate to rest.
In summary, based on the information given, the velocity-time graph will have the following shape:
- From 0 to 5 seconds: A diagonal line increasing linearly from 0 m/s to 25 m/s, representing the acceleration stage.
- From 5 to 20 seconds: A horizontal line at 25 m/s, representing the constant velocity stage.
- From 20 to 25 seconds: A diagonal line decreasing linearly from 25 m/s to 0 m/s, representing the deceleration stage.
Please note that the exact scaling of the graph may vary depending on the units used.
phase 1
v = 5 t , slope up of 5 up to Vi = 25
phase 2
v = constant = 25 from t = 5 to t = 20
phase 3
v = 25- 5(t-20), slope down of -5