To determine the speed at which the object is moving and the time it takes to reach that velocity, we can use the equations of motion.
Given: Initial velocity (u) = 0 m/s (starting from rest) Acceleration (a) = 4 m/s² Distance (s) = 200 m
We can use the equation of motion:
v² = u² + 2as
where: v = final velocity u = initial velocity a = acceleration s = distance
First, let's calculate the final velocity (v):
v² = u² + 2as v² = 0² + 2(4 m/s²)(200 m) v² = 0 + 2(800 m²/s²) v² = 1600 m²/s²
Taking the square root of both sides to solve for v:
v = √(1600 m²/s²) v = 40 m/s
Therefore, the object is moving at a speed of 40 m/s at that time.
Next, let's calculate the time it takes for the object to reach that velocity.
We can use the equation of motion:
v = u + at
Substituting the known values:
40 m/s = 0 m/s + (4 m/s²)t
Simplifying the equation:
40 m/s = 4 m/s² * t
Dividing both sides by 4 m/s²:
10 s = t
Therefore, it takes 10 seconds for the object to reach a velocity of 40 m/s.
To summarize:
- The object is moving at a speed of 40 m/s.
- It takes 10 seconds for the object to reach that velocity.