Answer:
The average speed of an object is given by the total distance traveled divided by the total time taken.
In this case, the particle is accelerated uniformly from rest to a speed of 50 meters per second in 5.0 seconds. Since it started from rest, we can use the formula for uniformly accelerated motion:
\[v = u + at\]
where:
- \(v\) is the final velocity (50 m/s)
- \(u\) is the initial velocity (0 m/s, as it starts from rest)
- \(a\) is the acceleration
- \(t\) is the time (5.0 seconds)
Rearranging the formula to solve for acceleration:
\[a = \frac{v - u}{t} = \frac{50 m/s - 0 m/s}{5.0 s} = 10 m/s^2\]
Next, we can use the formula for distance traveled with uniform acceleration:
\[s = ut + \frac{1}{2}at^2\]
Since the initial velocity is 0 m/s, this simplifies to:
\[s = \frac{1}{2}at^2 = \frac{1}{2} \times 10 m/s^2 \times (5.0 s)^2 = 125 m\]
So, the total distance traveled is 125 meters.
Now, we can calculate the average speed:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{125 m}{5.0 s} = 25 m/s\]
The average speed of the particle during this 5.0-second time interval is \(25 \, \text{m/s}\).
Therefore, the correct option is c) 25 m/s.¹1
Step-by-step explanation: