give answer in 2 step with all parts explanation at the end of each step and final answer at the end: A small toy car is being tested on a straight track in a

Question

give answer in 2 step with all parts explanation at the end of each step and final answer at the end:                                           A small toy car is being tested on a straight track in a school laboratory. The car starts from rest at one end of the track. A student gently pushes the car, giving it a light and steady acceleration. The total length of the track is $\ mathbf(5) $ meters, and the car reaches the other end of the track in exactly 10 seconds. Since the push is gentle and smooth, the car is assumed to move with uniform (constant) acceleration the entire time.

The purpose of this exercise is to determine the acceleration of the toy car as it moves along the track. The student wants to understand basic motion, so no friction, no air resistance, and no additional forces are considered. Only the initial rest position and the time taken to travel the distance are used.

For motion starting from rest with constant acceleration, the relationship between distance, acceleration, and time is:

s = \frac{1}2} at^{2}

where:

- $s = $ distance travelled (meters)

- $a = $ acceleration $ \left(\mathrm{m} / \mathrm{s} ^{2}\right) $

- $t = $ time

VIPSolutions · Accepted Answer

# Step 1: Write Down the Known Values

From the problem statement, we know:
- Distance travelled, $ s = 5 $ meters
- Time taken, $ t = 10 $ seconds
- Initial velocity, $ u =  $ (since the car starts from rest)

**Explanation:**  
These are the values provided:
- The car starts from rest, so initial velocity is zero.
- The total distance traveled is 5 meters.
- The total time taken is 10 seconds.

---

# Step 2: Substitute Values into the Formula and Solve for Acceleration

The formula for distance with constant acceleration from rest is:
$$
s = \frac{1}{2} a t^2
$$

Plug in the values:
$$
5 = \frac{1}{2} a (10)^2
$$

$$
5 = \frac{1}{2} a \times 100
$$

$$
5 = 50a
$$

$$
a = \frac{5}{50}
$$

$$
a = .1 \ \mathrm{m/s^2}
$$

**Explanation:**  
- Substituted $ s = 5 $, $ t = 10 $ into the equation.
- Simplified $ (10)^2 = 100 $.
- Solved the resulting equation for $ a $.

---

# Final Answer

**The acceleration of the toy car is:**  
$$
\boxed{.1 \ \mathrm{m/s^2}}
$$

VIPSolutions · Answer

# Step 1: Write Down the Known Values

From the problem statement, we know:

- **Distance travelled**: $ s = 5 $ meters
- **Time taken**: $ t = 10 $ seconds
- **Initial velocity**: $ u = 0 $ m/s (since the car starts from rest)

**Explanation:**  
These values are essential to apply the motion formula. The car's initial velocity is zero because it starts from rest. The total distance and time are given as 5 meters and 10 seconds, respectively.

---

# Step 2: Substitute Values into the Formula and Solve for Acceleration

The formula for distance with constant acceleration from rest is:
$$
s = \frac{1}{2} a t^2
$$

Substituting the known values:
$$
5 = \frac{1}{2} a (10)^2
$$

Calculating:
$$
5 = \frac{1}{2} a \times 100
$$
$$
5 = 50a
$$

Now, solving for $ a $:
$$
a = \frac{5}{50}
$$
$$
a = 0.1 \ \mathrm{m/s^2}
$$

**Explanation:**  
We substituted $ s $ and $ t $ into the equation, simplified $ (10)^2 $ to 100, and set up an equation to isolate $ a $. Finally, we calculated the acceleration.

---

# Final Answer

**The acceleration of the toy car is:**  
$$
\boxed{0.1 \ \mathrm{m/s^2}}
$$

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