a particle moves along the x-axis (units in cm) its initial position at t=0 sec is x(0)=15. the figure shows the graph of the particle's velocity v(t). the numbers are areas of the enclosed regions.
in the graph 0 to a is 4 under the x-axis, a to b is 5 above the x-axis, b to c is 24 under the x-axis.
what is the particle's displacement between t=0 and t=c?
To find the particle's displacement between t=0 and t=c, we need to consider the graph of its velocity.
The area under the velocity-time graph represents the displacement of the particle. Positive areas above the x-axis represent displacement in the positive direction, while negative areas below the x-axis represent displacement in the negative direction.
In this case, we have three regions:
- The area from 0 to a, which is 4 cm² under the x-axis. This represents a negative displacement.
- The area from a to b, which is 5 cm² above the x-axis. This represents a positive displacement.
- The area from b to c, which is 24 cm² under the x-axis. This represents a negative displacement.
To calculate the total displacement, we need to add up the areas:
Total displacement = (area from 0 to a) + (area from a to b) + (area from b to c)
= -4 + 5 - 24
= -23 cm²
Therefore, the particle's displacement between t=0 and t=c is -23 cm.