the driver of a car travelling at 100km/hr suddenly sight an obstacle 50m ahead of him What maximum acceleration must be applied to the car by applying the brake in order to avoid hitting the obstacle
100 km/hr = 27.78 m/s
v = √(2as)
27.78 = √(100a)
a = 7.716 m/s^2
That is the minimum acceleration which will do the job. There is no maximum value.
To determine the maximum acceleration required to avoid hitting the obstacle, we can use the equations of motion. Here are the steps:
Step 1: Convert the speed from kilometers per hour (km/hr) to meters per second (m/s). Since 1 km/hr is equal to 1000 m/3600 s, the speed is calculated as:
Speed = 100 km/hr × (1000 m/3600 s)
Speed = 100 × 1000 / 3600
Speed ≈ 27.78 m/s
Step 2: Use the first equation of motion, which relates acceleration, initial velocity, final velocity, and displacement:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, as the car should come to a stop)
u = initial velocity (27.78 m/s)
s = displacement (distance to the obstacle, 50 m)
a = acceleration
Substitute the given values into the equation:
0 = (27.78 m/s)^2 + 2a(50 m)
0 = 771.86 m^2/s^2 + 100a
Step 3: Rearrange the equation to solve for acceleration:
100a = -771.86 m^2/s^2
a = -771.86 m^2/s^2 / 100
Step 4: Calculate the acceleration:
a ≈ -7.72 m/s^2
Therefore, to avoid hitting the obstacle, the maximum acceleration that must be applied to the car by applying the brake is approximately 7.72 m/s^2. Note that negative acceleration is used because it corresponds to deceleration or slowing down the car.
To calculate the maximum acceleration required to avoid hitting the obstacle, we can use the kinematic equation:
vf^2 = vi^2 + 2ad
Where:
vf = final velocity (0 m/s, since we need to stop)
vi = initial velocity (100 km/hr, converts to 27.78 m/s)
d = distance (50 m)
a = acceleration
Rearranging the equation to solve for acceleration:
a = (vf^2 - vi^2) / (2d)
Plugging in the values we have:
a = (0^2 - 27.78^2) / (2 * 50)
Simplifying the equation:
a = (-27.78^2) / 100
a = -7.68 m/s²
The negative sign indicates that the acceleration is in the opposite direction of the car's initial velocity, or deceleration. Therefore, the maximum acceleration required to avoid hitting the obstacle is 7.68 m/s².