### Distance Calculation from Acceleration-Time Graph**Question:**12. The following graph is the acceleration versus time for the motion of a bike. If the bike starts from the origin with initial velocity 4.0 m/s, what is the total distance it travels during the 5.0 seconds of motion?**Graph Explanation:**The graph provided is a plot of acceleration (a) versus time (t). The x-axis represents time in seconds (s), ranging from 0 to 5 seconds. The y-axis represents acceleration in meters per second squared (m/s²), ranging from -1.5 to 2.5 m/s². Points plotted on the graph are as follows:- At t = 0 s, a ≈ 2.- At t = 1 s, a exists (though the exact value isn't required for calculating total displacement).- At t = 2 s, a ≈ -1.- At t = 3 s, a ≈ -1.5.- At t = 4 s, a ≈ -1.- At t = 5 s, a ≈ -1.**Solution Explanation:**To find the total distance travelled by the bike, we need to perform the following steps:1. **Understand the Initial Conditions**: The bike starts from the origin with an initial velocity of 4.0 m/s.2. **Use the Area Under the Graph**: The area under the acceleration-time graph provides the change in velocity.3. **Calculate Velocity at Various Points**: - For t = 0 to t = 1, the area is approximately 2 * 1 = 2 m/s²·s (positive area). - For t = 1 to t = 2, the area is approximately (-1) * 1 = -1 m/s²·s (negative area). - For t = 2 to t = 3, the area is approximately (-1.5) * 1 = -1.5 m/s²·s (negative area). - For t = 3 to t = 4, the area is approximately (-1) * 1 = -1 m/s²·s (negative area). - For t = 4 to t = 5, the area is approximately (-1) * 1 = -1 m/s²·s (negative area).

Name: ### Distance Calculation from Acceleration-Time Graph**Question:**12.
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: ### Distance Calculation from Acceleration-Time Graph**Question:**12. The following graph is the acceleration versus time for the motion of a bike. If the bike starts from the origin with initial velocity 4.0 m/s, what is the total distance it trave