A particle moving at 25 m/s in a straight line slows uniformly at a rate of 2 m/s every second. In an interval of 10 s, and: (a) the acceleration, (b) the final velocity, (c) the distance moved.
To solve this problem, we can use the following equations:
(a) Acceleration (a) is the rate at which velocity changes over time and is given by the equation:
a = (change in velocity) / (time)
In this case, the velocity decreases by 2 m/s every second, so the acceleration is -2 m/s² (negative because it is slowing down).
(a) Acceleration = -2 m/s²
(b) Final velocity (v) can be calculated using the equation:
v = initial velocity + (acceleration * time)
In this case, the initial velocity is 25 m/s, the acceleration is -2 m/s², and the time is 10 s.
(b) Final velocity = 25 m/s + (-2 m/s² * 10 s)
Final velocity = 25 m/s - 20 m/s
Final velocity = 5 m/s
(c) To calculate the distance moved, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time²)
Here, the initial velocity is 25 m/s, the time is 10 s, and the acceleration is -2 m/s².
(c) Distance moved = (25 m/s * 10 s) + (0.5 * -2 m/s² * (10 s)²)
Distance moved = 250 m - 100 m
Distance moved = 150 m
Therefore:
(a) The acceleration is -2 m/s².
(b) The final velocity is 5 m/s.
(c) The distance moved is 150 m.