A car accelerates from rest at 5 m/s^2 for 5 seconds. It moves with a constant velocity for some time, and then decelerates at 5 m/s^2 to come to rest. The entire journey takes 25 seconds. Plot the velocity-time graph of the motion.
They don't give me a graph so I made one. I have the velocity (vertical)going from 2-14 and the time (horizontal) going from 5-50. I'm not sure on where to start plotting, maybe my graph is a little off.
Your graph is more than a little off.
Take the equations, make a data table, and plot.
velocity time
0 0
5 1
10 2
and so on. In case you don't know
velocity= initial veloctiy + acceleration*time
To plot the velocity-time graph, we need to break down the journey into three different phases: acceleration, constant velocity, and deceleration.
Phase 1: Acceleration
The car accelerates from rest at 5 m/s^2 for 5 seconds. To determine its final velocity in this phase, we can use the kinematic equation:
vf = vi + at,
where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.
Since the car starts from rest (vi = 0) and accelerates at 5 m/s^2 for 5 seconds, the final velocity for this phase would be:
vf = 0 + (5 m/s^2)(5 s) = 25 m/s.
Phase 2: Constant Velocity
The car moves with a constant velocity for some time. During this phase, the velocity remains constant at 25 m/s. The duration of this phase can be calculated by subtracting the durations of Phases 1 and 3 from the total time: 25 seconds - 5 seconds (acceleration) - 5 seconds (deceleration) = 15 seconds.
Phase 3: Deceleration
The car decelerates at a constant rate of 5 m/s^2 until it comes to rest. In this phase, the initial velocity (vi) is 25 m/s, and the final velocity (vf) is 0 m/s. Using the same kinematic equation mentioned earlier, we can find the duration of deceleration as follows:
vf = vi + at => 0 = 25 m/s + (-5 m/s^2)(t)
Solving for t, we get t = 5 seconds.
Now, let's plot the velocity-time graph using the calculated values:
- At t = 0 seconds, the velocity is 0 m/s (starting point).
- From t = 0 seconds to t = 5 seconds, the velocity increases uniformly from 0 m/s to 25 m/s with an acceleration of 5 m/s^2 (phase 1).
- From t = 5 seconds to t = 20 seconds, the velocity remains constant at 25 m/s (phase 2).
- From t = 20 seconds to t = 25 seconds, the velocity decreases uniformly from 25 m/s to 0 m/s with a deceleration of -5 m/s^2 (phase 3).
Based on this information, you can adjust your graph accordingly, ensuring that the values of time and velocity are appropriately represented on the axes.