To determine the distance covered by a body in the last 2 seconds of motion, given that it starts from rest and travels for 100 seconds with a uniform acceleration of 1.5 m/s², we can use the equations of motion.
Let's break down the problem step by step:
- Determine the final velocity of the body after 100 seconds: Using the equation v = u + at, where: v = final velocity (unknown) u = initial velocity (0 m/s, since it starts from rest) a = acceleration (1.5 m/s²) t = time (100 s)
v = u + at v = 0 + (1.5 m/s²)(100 s) v = 150 m/s
- Determine the distance covered in the last 2 seconds: We know that the body starts from rest and travels for 100 seconds, so the total distance covered in 100 seconds can be calculated using the equation:
s = ut + (1/2)at², where: s = distance (unknown) u = initial velocity (0 m/s) t = time (100 s) a = acceleration (1.5 m/s²)
s = (0)(100 s) + (1/2)(1.5 m/s²)(100 s)² s = 0 + (1/2)(1.5 m/s²)(10000 s²) s = 0 + 0.5(1.5 m/s²)(10000 s²) s = 0 + 0.5(15000 m) s = 0 + 7500 m s = 7500 m
So, the body covers a distance of 7500 meters in the first 100 seconds of motion.
Now, to determine the distance covered in the last 2 seconds, we subtract the distance covered in the first 98 seconds (100 seconds - 2 seconds):
Distance covered in the last 2 seconds = Total distance - Distance covered in the first 98 seconds Distance covered in the last 2 seconds = 7500 m - s
Therefore, the distance covered in the last 2 seconds is 7500 meters minus the distance covered in the first 98 seconds.