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 35.57 meters before getting onto the bridge.
Explanation:
The problem involves uniformly accelerated motion. The car starts from rest and accelerates at 1.5 m/s² until it reaches the bridge. Once on the bridge, it takes 2.1 seconds to cross a 25-meter-long section.
- Find the velocity at the start of the bridge
We use the equation of motion:
[
s = v t + \frac{1}{2} a t^2
]
Substituting the given values for the bridge:
[
25 = v \times 2.1 + \frac{1}{2} \times 1.5 \times (2.1)^2
]
Solving for ( v ), we get:
[
v = 9.44 \text{ m/s}
]
This is the velocity just before entering the bridge. - Find the distance traveled before reaching the bridge
Using the kinematic equation:
[
v^2 = u^2 + 2 a s
]
Since the car starts from rest (( u = 0 )), we solve for ( s ):
[
9.44^2 = 2 \times 1.5 \times s
]
[
s = \frac{9.44^2}{2 \times 1.5} = 35.57 \text{ m}
]
Thus, the car traveled 35.57 meters before reaching the bridge.