A car is initially travelling at 50.0 km/h. The brakes are applied and the car stops over a distance of 35 m. What was magnitude of the car's acceleration while it was braking ?

Options

A. `2.8 m//s^(2)`
B. `5.4 m//s^(2)`
C. `36 m//s^(2)`
D. `71 m//s^(2)`

Answer

To find the magnitude of the car's acceleration while it was braking, we can follow these steps:

### Step 1: Convert the initial velocity from km/h to m/s
The initial velocity \( u \) is given as 50.0 km/h. We need to convert this to meters per second (m/s) using the conversion factor \( 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \).

\[ u = 50.0 \text{ km/h} \times \frac{5}{18} = \frac{250}{18} \approx 13.89 \text{ m/s} \]

### Step 2: Identify the final velocity
Since the car comes to a stop, the final velocity \( v \) is 0 m/s.

\[ v = 0 \text{ m/s} \]

### Step 3: Identify the distance traveled
The distance \( s \) over which the car stops is given as 35 m.

\[ s = 35 \text{ m} \]

### Step 4: Use the kinematic equation
We can use the kinematic equation that relates initial velocity, final velocity, acceleration, and distance:

\[ v^2 = u^2 + 2as \]

Substituting the known values into the equation:

\[ 0 = (13.89)^2 + 2a(35) \]

### Step 5: Rearranging the equation to solve for acceleration
Rearranging the equation to isolate \( a \):

\[ 0 = 192.61 + 70a \]
\[ 70a = -192.61 \]
\[ a = \frac{-192.61}{70} \approx -2.75 \text{ m/s}^2 \]

### Step 6: Find the magnitude of acceleration
Since we are asked for the magnitude of the acceleration, we take the absolute value:

\[ |a| \approx 2.75 \text{ m/s}^2 \]

### Final Answer
The magnitude of the car's acceleration while it was braking is approximately **2.75 m/s²**.

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