To determine the time taken for the object to travel a distance of 20m with a constant velocity of 5 m/s², we can use the equation of motion:
Distance = Initial velocity * time + (1/2) * acceleration * time²
Given: Initial velocity (u) = 10 m/s Acceleration (a) = 5 m/s² Distance (s) = 20 m
Using the equation above, we can rearrange it to solve for time (t):
s = ut + (1/2) * a * t²
Substituting the given values:
20 = 10t + (1/2) * 5 * t²
20 = 10t + (5/2) * t²
Multiplying the equation by 2 to eliminate fractions:
40 = 20t + 5t²
Rearranging the equation:
5t² + 20t - 40 = 0
Dividing the equation by 5:
t² + 4t - 8 = 0
Now, we can solve this quadratic equation using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 4, and c = -8.
t = (-4 ± √(4² - 4(1)(-8))) / (2 * 1)
t = (-4 ± √(16 + 32)) / 2
t = (-4 ± √48) / 2
t = (-4 ± 4√3) / 2
t = -2 ± 2√3
Therefore, the time taken to travel 20m is approximately:
t ≈ -2 - 2√3 or t ≈ -2 + 2√3
Since time cannot be negative in this context, the time taken to travel 20m is:
t ≈ -2 + 2√3 ≈ 0.464 seconds (rounded to three decimal places)