The figure gives the acceleration a versus time t for a particle moving along an x axis. The a-axis scale is set by as = 15.0 m/s2. At t = -2.0 s, the particle's velocity is 9.00 m/s. What is its velocity at t = 6.0 s?
since a is apparently not constant, and all you provide is a single data point, it's hard to determine the velocity at any other time.
To find the velocity of the particle at t = 6.0 s, we need to integrate the acceleration-time graph to obtain the velocity-time graph. Here's how you can do it:
1. Start by finding the area under the acceleration-time graph from t = -2.0 s to t = 6.0 s. Since the graph is a constant acceleration of 15.0 m/s^2, the area will simply be a rectangle.
2. Determine the height of the rectangle. The a-axis scale is set by as = 15.0 m/s^2, so the height of the rectangle is 15.0 m/s^2.
3. Find the width of the rectangle. The width is the time interval from t = -2.0 s to t = 6.0 s, which is 8.0 s.
4. Calculate the area of the rectangle by multiplying the height and width: Area = height x width = 15.0 m/s^2 x 8.0 s = 120.0 m/s.
5. The area under the velocity-time graph represents the change in velocity. Since the particle's velocity is 9.00 m/s at t = -2.0 s, we can determine the velocity at t = 6.0 s by adding the change in velocity to the initial velocity:
Velocity at t = 6.0 s = Initial velocity + Change in velocity
= 9.00 m/s + 120.0 m/s
= 129.0 m/s.
Therefore, the velocity of the particle at t = 6.0 s is 129.0 m/s.