A car slows down from 23m/s to rest in a distance of 85m. What was its acceleration, assumed constant?
The correct answer and explanation is :
To determine the acceleration of the car, we can use the kinematic equation:
[
v^2 = u^2 + 2as
]
where:
- ( v ) = final velocity = 0 m/s (since the car comes to rest),
- ( u ) = initial velocity = 23 m/s,
- ( s ) = displacement = 85 m,
- ( a ) = acceleration (to be determined).
Step 1: Rearrange the Formula
Rearranging the equation to solve for acceleration ( a ):
[
a = \frac{v^2 – u^2}{2s}
]
Step 2: Substitute the Given Values
[
a = \frac{(0)^2 – (23)^2}{2(85)}
]
[
a = \frac{0 – 529}{170}
]
[
a = \frac{-529}{170}
]
[
a = -3.11 \text{ m/s}^2
]
Step 3: Interpret the Result
The negative sign indicates that the acceleration is in the opposite direction to the motion of the car, meaning it is deceleration (slowing down). The magnitude of the acceleration is 3.11 m/s².
Explanation:
Acceleration is the rate of change of velocity. In this case, the car is experiencing a constant deceleration as it slows from 23 m/s to rest over a distance of 85 meters. The kinematic equation used accounts for uniformly accelerated motion, which assumes that the deceleration is constant throughout the motion.
The key takeaway here is that the acceleration value tells us how quickly the car reduces its speed. A larger magnitude of acceleration would indicate a quicker stop, whereas a smaller magnitude would indicate a more gradual stop. The negative sign simply signifies that the acceleration is in the direction opposite to the car’s initial velocity.
This type of calculation is useful in physics and engineering, particularly in designing safe stopping distances for vehicles and understanding braking performance.