A 2200kg vehicle travelling at 94k/h can be stopped in 21s by gently applying the brakes. It can be stopped in 3.8s if the driver slams on the brake. What average force is exerted on the vehicle in both of these stops?
To find the average force exerted on the vehicle in both stops, we need to use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
First, let's calculate the acceleration for each scenario:
Scenario 1: Gentle braking
Given:
Mass of the vehicle (m) = 2200 kg
Time to stop (t) = 21 s
To find acceleration (a), we can use the following formula:
a = Δv / t
Where:
Δv = change in velocity = final velocity - initial velocity
Initial velocity (u) = 94 km/h = 94,000 m/3600 s = 26.11 m/s (converting km/h to m/s)
Since the vehicle is stopping, the final velocity (v) is 0 m/s.
Δv = v - u
Δv = 0 - 26.11 m/s = -26.11 m/s (negative sign indicates the direction of motion is opposite to the initial velocity)
Now, we can calculate the acceleration (a):
a = Δv / t
a = (-26.11 m/s) / 21 s
a = -1.24 m/s^2
Scenario 2: Slamming on the brakes
Given:
Time to stop (t) = 3.8 s
Using the same formula as above, we need to find the change in velocity (Δv):
Δv = v - u
Since the vehicle is stopping, the final velocity (v) is 0 m/s.
Δv = v - u
Δv = 0 - 26.11 m/s = -26.11 m/s
Now, we can calculate the acceleration (a):
a = Δv / t
a = (-26.11 m/s) / 3.8 s
a = -6.87 m/s^2
Now that we have the acceleration values for both scenarios, we can use Newton's second law of motion to find the average force exerted on the vehicle:
Force = mass * acceleration
Scenario 1: Gentle braking
Force = 2200 kg * (-1.24 m/s^2)
Force ≈ -2,730.91 N (negative sign indicates the force is in the opposite direction of motion)
Scenario 2: Slamming on the brakes
Force = 2200 kg * (-6.87 m/s^2)
Force ≈ -15,114 N (negative sign indicates the force is in the opposite direction of motion)
Therefore, the average force exerted on the vehicle during gentle braking is approximately 2,730.91 Newtons, while the average force during slamming on the brakes is approximately 15,114 Newtons.