Final answer:
To calculate the acceleration of a bike which decreases its speed from 35 m/s to 15 m/s over 112 m, the kinematic equation is used, yielding an acceleration of approximately -4.46 m/s².
Step-by-step explanation:
To find the acceleration of a bike that slows down from 35 m/s to 15 m/s over a distance of 112 m, with constant acceleration, we can use the kinematic equation:
v2 = u2 + 2as
Where:
- v is the final velocity (15 m/s),
- u is the initial velocity (35 m/s),
- a is the acceleration,
- s is the distance (112 m).
Plugging in the values and solving for a yields:
(15 m/s)2 = (35 m/s)2 + 2a(112 m)
225 m2/s2 = 1225 m2/s2 + 224a m2/s2
-1000 m2/s2 = 224a m2/s2
a = -1000 / 224 m/s2
a ≈ -4.46 m/s2 (negative indicates deceleration)
The bike's acceleration was approximately -4.46 m/s2.