A car starts from rest and accelerates at a constant 1.5 m/s2. Some time later, it takes 2.1 s to cross over a 25-meter long bridge. How far did the car travel before getting onto the bridge?
The correct answer and explanation is :
The car traveled approximately 35.57 meters before getting onto the bridge.
Explanation:
- Understanding the problem:
- The car starts from rest and accelerates at (1.5 \, \text{m/s}^2).
- It takes 2.1 seconds to cross a 25-meter bridge.
- We need to determine how far the car traveled before reaching the bridge.
- Finding the velocity at the start of the bridge:
- Using the equation for distance under constant acceleration:
[
s = v t + \frac{1}{2} a t^2
] - Plugging in values:
[
25 = v \cdot 2.1 + \frac{1}{2} \times 1.5 \times (2.1)^2
] - Solving for ( v ), we get:
[
v = 8.81 \text{ m/s}
]
- Finding the time taken to reach this velocity:
- Using the equation of motion:
[
v = u + at
] - Since ( u = 0 ), solving for ( t ):
[
8.81 = 1.5 t
]
[
t = 5.87 \text{ seconds}
]
- Finding the distance traveled before the bridge:
- Using the equation:
[
s = ut + \frac{1}{2} a t^2
] - Since ( u = 0 ), solving for ( s ):
[
s = \frac{1}{2} \times 1.5 \times (5.87)^2
]
[
s \approx 35.57 \text{ meters}
]
Thus, the car traveled 35.57 meters before reaching the bridge.