A car accelerates from rest with a uniform acceleration of 1.7m/s for 10 seconds, its acceleration then reduces by 0.3m/s for 20 seconds of the motion, it then maintains the speed attained for another 20 seconds after which it decelerates to rest within 10 seconds. Draw the velocity-time graph of the motion and hence calculate the magnitude of the velocity after 10 seconds and 30 seconds.
I don't know how todraw it on this forum. Plot velocity from the given information.
To draw the velocity-time graph of the motion, we need to break down the different phases of acceleration, constant velocity, and deceleration.
Phase 1: Acceleration
The car accelerates from rest at a uniform acceleration of 1.7 m/s² for 10 seconds. We know that acceleration is the rate of change of velocity, so we can use the equation:
v = u + at
where v is the final velocity, u is the initial velocity (which is 0 m/s since the car starts from rest), a is the acceleration (1.7 m/s²), and t is the time (10 seconds).
Calculating:
v = 0 + (1.7 × 10)
v = 17 m/s
So, after 10 seconds, the magnitude of the velocity is 17 m/s.
Phase 2: Decreasing acceleration
The acceleration of the car then reduces by 0.3 m/s² for 20 seconds. This means the constant acceleration during this phase is now 1.7 m/s² - 0.3 m/s² = 1.4 m/s². We can use the same formula to calculate the change in velocity during this phase:
v = u + at
where u is the final velocity of the previous phase (17 m/s), a is the acceleration (1.4 m/s²), and t is the time (20 seconds).
Calculating:
v = 17 + (1.4 × 20)
v = 17 + 28
v = 45 m/s
So, after 30 seconds, the magnitude of the velocity is 45 m/s.
Phase 3: Constant Velocity
The car then maintains the speed attained (45 m/s) for another 20 seconds. During constant velocity, there is no acceleration, so the velocity remains the same.
Phase 4: Deceleration to rest
Finally, the car decelerates to rest within 10 seconds. Deceleration is negative acceleration. To calculate the final velocity, we use the same formula as before:
v = u + at
where u is the initial velocity of this phase (45 m/s), a is the deceleration (which we need to find), and t is the time (10 seconds).
We know that the final velocity is 0 m/s:
0 = 45 + (a × 10)
10a = -45
a = -4.5 m/s²
The deceleration is -4.5 m/s².
Now we have all the information to draw the velocity-time graph.
Velocity-Time Graph:
Plotting the points:
At 0 seconds: Velocity is 0 m/s
At 10 seconds: Velocity is 17 m/s
At 30 seconds: Velocity is 45 m/s
At 50 seconds: Velocity is still 45 m/s
At 60 seconds: Velocity is 0 m/s
Connecting the points will give us the velocity-time graph.
|
45 _______⁄‾‾‾‾‾‾‾\_______
| |
20 | |
0 ___|____________________|___
10 30 50
The magnitude of the velocity after 10 seconds is 17 m/s, and after 30 seconds is 45 m/s.