To find the required acceleration to reduce the speed to 72 km/h, we can follow these steps:
Step 1: Convert the speed limit from km/h to m/s.
Speed limit = 72 km/h
1 km = 1000 m
1 hour = 3600 seconds
72 km/h = (72 * 1000 m) / (3600 s)
= 72,000 m / 3600 s
= 20 m/s
So, the speed limit is 20 m/s.
Step 2: Determine the initial velocity of the car.
Given that the motorist drives at 30 m/s along the road.
Initial velocity (u) = 30 m/s
Step 3: Calculate the change in velocity.
Change in velocity (ฮv) = Final velocity (v) - Initial velocity (u)
= 20 m/s - 30 m/s
= -10 m/s (negative sign indicates deceleration)
Step 4: Determine the distance required to achieve the desired change in velocity.
Given that the motorist applies brakes 25 m before the speed trap.
Distance (s) = 25 m
Step 5: Apply the formula to find acceleration (a).
The formula relating acceleration, change in velocity, and distance is:
ฮv^2 = 2as
Rearranging the formula to solve for acceleration (a):
a = ฮv^2 / (2s)
= (-10 m/s)^2 / (2 * 25 m)
= 100 m^2/s^2 / 50 m
= 2 m/s^2
Therefore, the acceleration required to reduce the speed to 72 km/h as the car reaches the speed trap is 2 m/s^2.