A car is moving with a velocity of 10 m/s. Suddenly driver sees a child at a distance of 30 m and he applies the brakes, it produced a uniform retardation in car and car stops in 5 second. Find (mass of car=1000 kg)
the stopping distance of car
will the car hit the child
the retardation in car
resistive force on car

Answer

To solve the problem step by step, we will find the stopping distance of the car, check if it hits the child, calculate the retardation, and finally determine the resistive force acting on the car.

### Step 1: Calculate the retardation
We know the initial velocity \( u = 10 \, \text{m/s} \), final velocity \( v = 0 \, \text{m/s} \), and time \( t = 5 \, \text{s} \).

Using the formula for acceleration (retardation in this case):
\[ a = \frac{v - u}{t} \]
Substituting the values:
\[ a = \frac{0 - 10}{5} = \frac{-10}{5} = -2 \, \text{m/s}^2 \]
Thus, the retardation is \( 2 \, \text{m/s}^2 \).

### Step 2: Calculate the stopping distance
We can use the equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting the known values:
\[ s = (10)(5) + \frac{1}{2}(-2)(5^2) \]
Calculating each term:
\[ s = 50 + \frac{1}{2}(-2)(25) \]
\[ s = 50 - 25 = 25 \, \text{m} \]
Thus, the stopping distance of the car is \( 25 \, \text{m} \).

### Step 3: Determine if the car will hit the child
The child is located \( 30 \, \text{m} \) away from the car when the brakes are applied. Since the stopping distance of the car is \( 25 \, \text{m} \), which is less than \( 30 \, \text{m} \), the car will not hit the child.

### Step 4: Calculate the resistive force on the car
Using Newton's second law, the resistive force \( F \) can be calculated as:
\[ F = m \cdot a \]
Where \( m = 1000 \, \text{kg} \) and \( a = -2 \, \text{m/s}^2 \):
\[ F = 1000 \cdot (-2) = -2000 \, \text{N} \]
The resistive force acting on the car is \( 2000 \, \text{N} \) in the direction opposite to the motion.

### Summary of Results:
1. **Stopping Distance of Car**: \( 25 \, \text{m} \)
2. **Will the Car Hit the Child?**: No
3. **Retardation in Car**: \( 2 \, \text{m/s}^2 \)
4. **Resistive Force on Car**: \( 2000 \, \text{N} \)