Question

a car, initially traveling 10ft/s steadily slows to a stop in 5.0s. determine all unknowns and answer the following question. how far did the car travel during this time?

Explanation:

Step1: Identify known quantities

Initial velocity \( v_i = 10 \, \text{m/s} \) (assuming unit is m/s), final velocity \( v_f = 0 \, \text{m/s} \) (stops), time \( t = 5.0 \, \text{s} \).

Step2: Find acceleration

Using \( a=\frac{v_f - v_i}{t} \), substitute values: \( a=\frac{0 - 10}{5.0}=-2 \, \text{m/s}^2 \).

Step3: Calculate distance

Use the formula \( d = v_i t+\frac{1}{2}at^2 \). Substitute \( v_i = 10 \), \( t = 5 \), \( a=-2 \):
\( d = 10\times5+\frac{1}{2}\times(-2)\times5^2 = 50 - 25 = 25 \, \text{m} \).
(Or use \( d=\frac{v_i + v_f}{2}t=\frac{10 + 0}{2}\times5 = 25 \, \text{m} \), simpler for constant acceleration.)

Filling unknowns:

• \( v_i = 10 \, \text{m/s} \)
• \( v_f = 0 \, \text{m/s} \)
• \( a=-2 \, \text{m/s}^2 \)
• \( t = 5.0 \, \text{s} \)
• Distance \( d = 25 \, \text{m} \)

Answer:

The car traveled \(\boldsymbol{25}\) meters (unit: meters, assuming initial velocity unit is m/s).
(For unknowns: \( v_i = 10 \, \text{m/s} \), \( v_f = 0 \, \text{m/s} \), \( a=-2 \, \text{m/s}^2 \), \( t = 5.0 \, \text{s} \), \( d = 25 \, \text{m} \))