If a racehorse starts from rest and accelerates at a rate of 4.7 m/s2, how long does it take the horse to go 20 m?
d = 1/2 a t^2
t = ā(2 * d * a)
9.1
To find the time it takes for the racehorse to go 20 m with an acceleration of 4.7 m/s^2, you can use the second equation of motion:
s = ut + (1/2)at^2,
Where:
- s is the distance traveled (20 m),
- u is the initial velocity (0 m/s, as the racehorse starts from rest),
- a is the acceleration (4.7 m/s^2),
- t is the time.
Since the racehorse starts from rest, the initial velocity (u) is 0. By substituting these values into the equation, we get:
20 = 0 + (1/2)(4.7)t^2.
Simplifying the equation:
20 = 2.35t^2.
To solve for t, divide both sides of the equation by 2.35:
t^2 = 20 / 2.35.
t^2 = 8.51.
Finally, take the square root of both sides to find t:
t = ā8.51.
Using a calculator, we find that t ā 2.92 seconds (rounded to two decimal places).
Therefore, it takes approximately 2.92 seconds for the racehorse to go 20 m with an acceleration of 4.7 m/s^2.