while cruising along dark stretch of highway at a speed of 25 m/s you see that bridge ahead has been washed out. you apply the breaks to and come to a stop in 4.0 sec
construct the position vs time graph and acceleration vs time graph and motion graph for 4 sec interval
Velocity
(m ⁄ sec)
↑
25 | \
| \
| \
| \
| \
| \ slope = acceleration
| \
| \
—— 0 |—ı—ı—ı—ı———→ Time (seconds)
0 4
a = (ΔV) ∕ (Δt) ... (change in velocity) ∕ (change in time)
a = (0 – 25) ∕ (4 – 0)
a = - 6.25 m/sec² ... acceleration is negative because it it slowing down
55 mph
To construct the position vs time graph and acceleration vs time graph for the given scenario, we need to analyze the motion of the car during the 4 second interval.
1. Position vs Time Graph:
The position vs time graph represents the change in position of the car over time. Since the car comes to a stop, the position vs time graph would be a straight line representing zero displacement (constant position) after the car comes to a stop.
At time t=0, the position of the car would be at a certain distance on the highway. As time passes, the position remains constant until the car comes to a stop at t=4 seconds. Therefore, the position vs time graph would be a straight line horizontally at a specific position until t=4 seconds, representing the distance covered by the car before coming to a stop.
2. Acceleration vs Time Graph:
To construct the acceleration vs time graph, we need to calculate the acceleration of the car during the deceleration phase.
Acceleration is given by the formula:
Acceleration = (Final velocity - Initial velocity) / Time
Given:
Initial velocity (u) = 25 m/s
Final velocity (v) = 0 m/s
Time (t) = 4 seconds
Acceleration = (0 - 25) / 4 = -25 / 4 = -6.25 m/s^2
Since the car decelerates uniformly with a constant acceleration, the acceleration vs time graph would be a straight line with a negative slope (-6.25 m/s^2) for the entire 4-second interval.
3. Motion Graph:
The motion graph represents the motion of the car, showing the velocity at each point in time.
Since the car starts with an initial velocity of 25 m/s and comes to a stop (final velocity = 0 m/s), the motion graph would be a straight line with a negative slope (-25 m/s) until t=4 seconds when the car comes to a stop.
Remember, the motion graph is the derivative of the position vs time graph, and the acceleration vs time graph is the derivative of the motion graph.
Note: To get more precise values and a more accurate graph, you might need additional data such as the distance covered by the car before coming to a stop.