Final answer:
To calculate the acceleration of a cheetah that goes from rest to 84 km/h over 50 m, we convert the speed to m/s and use the kinematic formula. This yields an acceleration of 5.44 m/s².
Step-by-step explanation:
The question asks for the acceleration of a cheetah that increases its speed from rest to 84 km/h over a distance of 50 m. To solve for acceleration, we need to use the kinematic equations of motion.
First, convert 84 km/h to m/s by multiplying by ≈ 0.27778 (since 1 km/h = 1/3.6 m/s). This gives us the final velocity (v) of 23.33 m/s (since 84 × 0.27778 = 23.33 m/s). Now, given that the initial velocity (u) is 0 m/s, final velocity (v) is 23.33 m/s, and displacement (s) is 50 m, we can use the formula:
v2 = u2 + 2as
Plugging in the values, we get:
23.332 = 02 + 2 × a × 50
Simplifying, we find the acceleration (a):
544.44 = 100a
·a = 544.44/100
·a = 5.44 m/s²
Therefore, the acceleration of the cheetah is 5.44 m/s².