A race horse starts from rest with an acceleration of 4.80m/s^2
1. How long does it take for the horse to reach a velocity of 32.0m/s?
2. Calculate the displacement of the horse
v = a t
32.0 = 4.8 t
t = 32/4.8
x = (1/2) a t^2
To answer these questions, we will make use of the equations of motion. The equation we will use is:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
1. How long does it take for the horse to reach a velocity of 32.0 m/s?
Given:
Initial velocity (u) = 0 m/s (starting from rest)
Acceleration (a) = 4.80 m/s^2
Final velocity (v) = 32.0 m/s
We need to substitute these values into the equation and solve for time (t). Rearranging the equation:
v = u + at
32.0 = 0 + (4.80)t
32.0 = 4.80t
Now, divide both sides of the equation by 4.80:
32.0/4.80 = t
6.67 = t
Therefore, it takes approximately 6.67 seconds for the horse to reach a velocity of 32.0 m/s.
2. Calculate the displacement of the horse.
To calculate displacement, we can use another equation of motion:
s = ut + (1/2)at^2
where:
s = displacement
u = initial velocity
t = time
a = acceleration
Given:
Initial velocity (u) = 0 m/s (starting from rest)
Acceleration (a) = 4.80 m/s^2
Time (t) = 6.67 seconds (from the previous question)
Substituting these values into the equation:
s = (0)(6.67) + (1/2)(4.80)(6.67)^2
Simplifying the equation:
s = 0 + (1/2)(4.80)(44.5)
Now multiply:
s ≈ 53.28 meters
Therefore, the displacement of the horse is approximately 53.28 meters.