(a) A car accelerates from 0 to 30.0 m s-1 in 6.0 seconds, travels at a constant 30.0 m s-1 for 21.0 seconds, and then brakes to a stop in 3.0 seconds.
(i) Draw a velocity-time graph illustrating this motion
(ii) Calculate the acceleration (assumed constant) in each section of the motion.
(iii) Calculate the distance travelled
(iv) Sketch a distance-time graph for the motion
(v) What is 30.0 m s-1 in km/hr?
(i) To draw a velocity-time graph illustrating this motion, we need to plot the velocity on the y-axis and time on the x-axis.
The motion can be divided into three sections:
1. From 0 to 6 seconds, the car accelerates from 0 to 30.0 m/s.
2. From 6 to 27 seconds, the car travels at a constant velocity of 30.0 m/s.
3. From 27 to 30 seconds, the car decelerates from 30.0 m/s to 0.
The graph will look like this:
y-axis = velocity (m/s)
x-axis = time (s)
|
30 +-------+
| __________________________
| _______________________
| __________________
|
|_______________________________
| | |
0 6 27
(ii) To calculate the acceleration in each section:
Section 1: Acceleration from 0 to 30.0 m/s in 6 seconds.
Acceleration = (final velocity - initial velocity) / time
Acceleration = (30.0 m/s - 0 m/s) / 6 seconds
Acceleration = 5.0 m/s²
Section 2: The car travels at a constant velocity of 30.0 m/s.
There is no acceleration as the velocity remains constant.
Section 3: Deceleration from 30.0 m/s to 0 m/s in 3 seconds.
Deceleration (negative acceleration) = (final velocity - initial velocity) / time
Deceleration = (0 m/s - 30.0 m/s) / 3 seconds
Deceleration = -10.0 m/s² (negative because the car is slowing down)
(iii) To calculate the distance traveled:
Section 1: Distance = (initial velocity * time) + (0.5 * acceleration * time²)
Distance = (0 m/s * 6 seconds) + (0.5 * 5.0 m/s² * (6 seconds)²)
Distance = 0 + (0.5 * 5.0 m/s² * 36 seconds²)
Distance = 90 meters
Section 2: Distance = velocity * time
Distance = 30.0 m/s * 21.0 seconds
Distance = 630 meters
Section 3: Distance = (initial velocity * time) + (0.5 * acceleration * time²)
Distance = (30.0 m/s * 3 seconds) + (0.5 * -10.0 m/s² * (3 seconds)²)
Distance = 90 meters
Total distance traveled = 90 meters + 630 meters + 90 meters = 810 meters
(iv) To sketch a distance-time graph, we need to plot the distance traveled on the y-axis and time on the x-axis.
The graph will look like a step function:
y-axis = distance traveled (m)
x-axis = time (s)
|
810 + _____
| |
| |
120 + |__________|
| |
0 +------+------------------+
0 6 27 30
(v) To convert 30.0 m/s to km/hr:
1 km = 1000 m
1 hour = 3600 seconds
30.0 m/s * (1 km/1000 m) * (3600 s/1 hr) = 108 km/hr
So, 30.0 m/s is equal to 108.0 km/hr.