A car is travelling 20m/s along a straight road. The driver sees a 36km/h speed limit sign 100m ahead. What constant retardation is required to reduce the speed to 36km/h in this distance. Find also the time taken by the car to reach the speed limit region.
vf^2=vi^2 + 2ad where a=force/mass
solve for a, then
time=changevelocity/a
To find the constant retardation required to reduce the car's speed to 36 km/h in 100m, we can use the following steps:
Step 1: Convert the car's initial speed from m/s to km/h.
- The car is traveling at 20 m/s.
- 1 m/s is equal to 3.6 km/h.
- Therefore, 20 m/s is equal to (20 × 3.6) km/h = 72 km/h.
Step 2: Determine the change in speed.
- The initial speed is 72 km/h, and the final speed is 36 km/h.
- The change in speed is equal to the final speed minus the initial speed.
- Therefore, the change in speed is 36 km/h - 72 km/h = -36 km/h.
(Note: We use a negative sign as the change in speed is a reduction.)
Step 3: Convert the change in speed from km/h to m/s.
- 1 km/h is equal to 0.2778 m/s (approximately).
- Therefore, the change in speed is (-36 × 0.2778) m/s = -10 m/s.
Step 4: Calculate the required retardation.
- The change in speed is equal to the product of the retardation and the distance.
- Therefore, -10 m/s = retardation × 100 m.
- Solving for retardation: retardation = (-10 m/s) / (100 m) = -0.1 m/s^2.
Hence, the constant retardation required to reduce the car's speed to 36 km/h in 100 m is -0.1 m/s^2 (negative indicating a deceleration).
To find the time taken by the car to reach the speed limit region, we can use the formula:
Time = Distance / Initial Speed
In this case, the distance is 100 m, and the initial speed is 20 m/s.
Time = 100 m / 20 m/s = 5 seconds
Therefore, the car will take 5 seconds to reach the speed limit region.