If your car accelerates from rest at a steady rate of 4 m/s2, how soon will it reach 84 km/h
V = 81km/h = 81000m/3600s = 22.5 m/s.
V = Vo + at = 22.5 m/s.
0 + 4*t = 22.5
t = 5.625 s.
To determine how soon the car will reach a speed of 84 km/h, we need to convert the given speed from km/h to m/s and use the equation of motion relating acceleration, initial velocity, time, and final velocity.
Step 1: Convert the final speed from km/h to m/s.
To convert km/h to m/s, we can use the conversion factor 1 km/h = 0.2778 m/s.
So, 84 km/h = 84 * 0.2778 m/s = 23.3332 m/s (approximately)
Step 2: Use the equation of motion to solve for time.
The equation of motion that relates acceleration, initial velocity, time, and final velocity is:
final velocity = initial velocity + (acceleration * time)
We know:
initial velocity = 0 m/s (the car starts from rest)
acceleration = 4 m/s^2
final velocity = 23.3332 m/s
Plugging these values into the equation, we have:
23.3332 = 0 + (4 * time)
Simplifying the equation:
23.3332 = 4t
Step 3: Solve for time.
Dividing both sides of the equation by 4, we get:
t = 23.3332 / 4
t ≈ 5.8333 s
Therefore, the car will reach a speed of 84 km/h in approximately 5.8333 seconds.