Question

A car starts from rest and accelerates uniformly to a speed of 180 km/h in 10 s. The distance covered by the car in this time interval is

• A. 500 m
• B. 250 m
• C. 100 m
• D. 200 m

Hint:

When solving for distance in uniformly accelerated motion, use the equation \( s = \frac{1}{2} a t^2 \), where \( a \) is the acceleration and \( t \) is the time. Ensure you convert all units to the standard SI units before calculating.

Answer 1

The Correct Option is B

We are given the following information: - The car starts from rest, so initial velocity \( u = 0 \). 
- The final velocity \( v = 180 \, \text{km/h} = 180 \times \frac{1000}{3600} \, \text{m/s} = 50 \, \text{m/s} \). 
- The time interval \( t = 10 \, \text{s} \). We need to find the distance covered by the car in this time. 
Using the equation of motion for uniformly accelerated motion: \[ s = ut + \frac{1}{2} a t^2 \] 
Since the initial velocity \( u = 0 \), the equation simplifies to: \[ s = \frac{1}{2} a t^2 \] 
To find the acceleration \( a \), we use the equation: \[ v = u + at \] Substitute the known values: \[ 50 = 0 + a \times 10 \] Solving for \( a \): \[ a = \frac{50}{10} = 5 \, \text{m/s}^2 \] Now, substitute \( a = 5 \, \text{m/s}^2 \) and \( t = 10 \, \text{s} \) into the equation for distance: \[ s = \frac{1}{2} \times 5 \times 10^2 = \frac{1}{2} \times 5 \times 100 = 250 \, \text{m} \] 
Thus, the distance covered by the car is 250 m. Therefore, the correct answer is: \[ \text{(B) } 250 \, \text{m} \]

Answer 2

To solve this problem, we need to calculate the distance covered by a car that starts from rest and accelerates uniformly to a speed of 180 km/h in 10 seconds. We will use the kinematic equation:

s = ut + (1/2)at²

where:

• s is the distance covered,
• u is the initial velocity (0 m/s, since the car starts from rest),
• t is the time (10 s),
• a is the acceleration.

First, convert the final speed from km/h to m/s:

v = 180 km/h = (180 × 1000 m) / (3600 s) = 50 m/s

Next, use the formula for acceleration:

a = (v - u) / t = (50 m/s - 0 m/s) / 10 s = 5 m/s²

Finally, calculate the distance using the kinematic equation:

s = 0 × 10 + (1/2) × 5 × (10)² = (1/2) × 5 × 100 = 250 m

Thus, the distance covered by the car is 250 m.