A car travelling along a road begins accelerating with a constant acceleration of `1.5 m//s^(2)` in the direction of motion. After travelling 392 m at this acceleration, its speed is 35 m/s. Determine the speed of the car when it began accelerating.

Options

A. 1.5 m/s
B. 34 m/s
C. 7.0 m/s
D. 49 m/s

Answer

To determine the speed of the car when it began accelerating, we can use the equations of motion. Here's a step-by-step solution:

### Step 1: Identify the known values
- Final velocity (V) = 35 m/s (the speed after acceleration)
- Acceleration (a) = 1.5 m/s²
- Distance travelled during acceleration (s) = 392 m

### Step 2: Use the equation of motion
We will use the third equation of motion, which relates initial velocity (u), final velocity (V), acceleration (a), and distance (s):
\[ V^2 = u^2 + 2as \]

### Step 3: Rearrange the equation to solve for initial velocity (u)
Rearranging the equation gives:
\[ u^2 = V^2 - 2as \]

### Step 4: Substitute the known values into the equation
Substituting the known values into the equation:
- V = 35 m/s
- a = 1.5 m/s²
- s = 392 m

So we have:
\[ u^2 = (35)^2 - 2 \times (1.5) \times (392) \]

### Step 5: Calculate the values
Calculating \( (35)^2 \):
\[ (35)^2 = 1225 \]

Calculating \( 2 \times (1.5) \times (392) \):
\[ 2 \times 1.5 = 3 \]
\[ 3 \times 392 = 1176 \]

Now substituting these values back into the equation:
\[ u^2 = 1225 - 1176 \]
\[ u^2 = 49 \]

### Step 6: Solve for u
Taking the square root of both sides:
\[ u = \sqrt{49} \]
\[ u = 7 \, \text{m/s} \]

### Conclusion
The speed of the car when it began accelerating was **7 m/s**.

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