Final answer:
To calculate 'm', we must analyze the velocity-time graph and set up equations for each of the three phases of the particle's motion. Using the given total displacement of 2000 meters, we can solve for 'm'. To find the driving force, we will use the formula F = ma but without exact values, we cannot complete the calculation.
Step-by-step explanation:
To answer the question, we must first calculate the value of 'm' using the information provided about the particle's motion. Since the particle covers a total distance of 2000 meters, we can divide its journey into three segments: acceleration, constant velocity, and deceleration. The particle starts from rest, accelerates for 10 seconds, moves with constant velocity for another 10 seconds, and finally decelerates to rest in 'm' seconds.
To draw a velocity-time graph, we'll represent the acceleration phase with a straight line increasing from 0 to 'm' m/s over the initial 10 seconds, a horizontal line for the next 10 seconds representing constant velocity, and then a line sloping down to 0 m/s over the period of 'm' seconds. The area under the velocity-time graph represents the total displacement.
From the description, we know the particle accelerates uniformly. Using the equation 's = ut + 1/2 at^2' where s is displacement, u is initial velocity, a is acceleration, and t is time, we can set up equations for each segment of the journey and solve for 'm'. For the second part regarding the driving force, we'll use Newton's second law, which states that force equals mass times acceleration (F = ma).
After solving the equations, we can find the value of the driving force exerted on the particle. It should be noted that we are not provided with sufficient information to solve this problem entirely; we would need additional equations derived from the specifics of the distance covered during each segment to calculate 'm'.