To calculate the distance traveled by an object in the next 10 seconds, we first need to determine the acceleration of the object. Given that the object started from rest and achieved a velocity of 20 m/s after 5 seconds, we can find the acceleration using the formula:
acceleration (a) = change in velocity / time taken
The change in velocity is 20 m/s (final velocity) - 0 m/s (initial velocity) = 20 m/s, and the time taken is 5 seconds. Therefore:
acceleration (a) = 20 m/s / 5 s = 4 m/s²
Once we have the acceleration, we can calculate the distance traveled using the kinematic equation:
distance (d) = initial velocity (u) * time (t) + (1/2) * acceleration (a) * time²
Since the object started from rest, the initial velocity is 0 m/s, and the time is 10 seconds. Plugging in these values:
distance (d) = 0 m/s * 10 s + (1/2) * 4 m/s² * (10 s)² = 0 + 0.5 * 4 m/s² * 100 s² = 0 + 0.5 * 4 m/s² * 100 s² = 0 + 2 m/s² * 100 s² = 200 m
Therefore, the object will travel a distance of 200 meters in the next 10 seconds.