A motorcycle is moving with a velocity of `90 km//h` and it takes `5 second` to stop after the brakers are applied. Calculate the force exerted by the brakers on the motorcycle if its mass alongwith the rider is `200 kg`

Options

A. -100 N
B. 500 N
C. 200 N
D. -1000 N

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert the velocity from km/h to m/s
The motorcycle is moving at a velocity of 90 km/h. To convert this to meters per second (m/s), we use the conversion factor \( \frac{5}{18} \).

\[ \text{Velocity in m/s} = 90 \times \frac{5}{18} = 25 \, \text{m/s} \]

### Step 2: Identify the initial and final velocities
- Initial velocity (\( u \)) = 25 m/s (as calculated above)
- Final velocity (\( v \)) = 0 m/s (since the motorcycle comes to a stop)

### Step 3: Determine the time taken to stop
The time taken (\( t \)) to stop is given as 5 seconds.

### Step 4: Use the first equation of motion to find acceleration
We can use the first equation of motion:

\[ v = u + at \]

Substituting the known values:

\[ 0 = 25 + a \times 5 \]

Rearranging the equation to solve for acceleration (\( a \)):

\[ a \times 5 = -25 \]
\[ a = -\frac{25}{5} = -5 \, \text{m/s}^2 \]

### Step 5: Calculate the force exerted by the brakes
Using Newton's second law of motion, the force (\( F \)) can be calculated using the formula:

\[ F = m \times a \]

Where:
- \( m \) = mass of the motorcycle and rider = 200 kg
- \( a \) = acceleration = -5 m/s²

Substituting the values:

\[ F = 200 \times (-5) = -1000 \, \text{N} \]

### Step 6: Interpret the result
The negative sign indicates that the force exerted by the brakes is in the opposite direction to the motion of the motorcycle.

### Final Answer
The force exerted by the brakes on the motorcycle is \( 1000 \, \text{N} \) (opposing the motion).

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