A car starts from rest is uniformly accelerated at 0.1m/s square untill it reaches a speed of 15m/sec square. It travels at this speed for 3mins and it returns uniformly retarded so as it come to rest 8mins after starting.plot the velocity time graph of the motion and use the graph to determine
speed is m/s
v = at
it accelerated for 15/.1 = 150 seconds
after another 150 seconds, until t=150 s = 5 min. Then it decelerated for the remaining 3 minutes, or 180 seconds. That means it decelerated at 15/180 = 1/12 m/s^2
v(t) =
t/10 for 0 <= t <= 150
15 for 150 < t < 300
15 - (t-300)/12 for 300 <= t <= 480
To plot the velocity-time graph of the motion, we can divide the problem into three phases: acceleration, constant velocity, and deceleration.
1. Acceleration:
The car starts from rest and accelerates uniformly at a rate of 0.1 m/s^2 until it reaches a speed of 15 m/s. We can calculate the time it takes to reach this speed using the formula:
Final velocity = Initial velocity + (Acceleration * Time)
15 m/s = 0 m/s + (0.1 m/s^2 * Time)
Time = 150 seconds
So, it takes 150 seconds for the car to reach a speed of 15 m/s. During this time, the velocity is increasing uniformly, so the velocity-time graph will be a straight line with a positive slope.
2. Constant Velocity:
The car travels at a constant speed of 15 m/s for 3 minutes, which is equal to 180 seconds. During this phase, the car's velocity remains constant, so the velocity-time graph will be a horizontal straight line.
3. Deceleration:
After traveling at a constant speed, the car begins to decelerate uniformly until it comes to a rest. The time it takes to come to rest can be determined using the formula mentioned earlier:
Final velocity = Initial velocity + (Acceleration * Time)
0 m/s = 15 m/s + (Acceleration * Time)
Time = -150 seconds
The negative sign indicates that the car is decelerating. The time is -150 seconds, which is equivalent to 150 seconds in the opposite direction. So, it takes 150 seconds for the car to come to a rest. During this deceleration phase, the velocity will decrease uniformly, resulting in a negative slope on the velocity-time graph.
To summarize, the velocity-time graph would look like this:
|
15 |
| |
| |
| |\
| \
0 |__\__
The upward-sloping line represents the acceleration phase, the horizontal line represents the constant velocity phase, and the downward-sloping line represents the deceleration phase.
To determine specific values from the graph:
- The time it takes for the car to reach a velocity of 10 m/s can be read from the graph as the x-coordinate where the velocity intersects 10 m/s on the acceleration phase.
- The time it takes for the car to come to rest after it starts can be read from the graph as the x-coordinate where the velocity intersects the x-axis on the deceleration phase.