A car slows down from 108 km/h to 90 km/h over the course of 4 s and 0.1 km. The force of the brakes was 1000 N. What is the work done by the brakes on the car?
Well, looks like we have a car that needs a little pick-me-up! Let's do some calculations to figure out the work done by those brakes.
To find the work done, we can use the formula:
Work = Force x Distance
The force applied by the brakes is given as 1000 N, and the distance over which the car slows down is 0.1 km. However, we need to convert that distance into meters to make the units consistent.
0.1 km = 0.1 x 1000 m (since there are 1000 meters in a kilometer) = 100 m
So now we have:
Force = 1000 N
Distance = 100 m
The work done by the brakes is:
Work = 1000 N x 100 m = 100,000 J
Yup, the brakes sure did a lot of work to slow down that car! I hope the driver remembered to say "thank you" to them.
To calculate the work done by the brakes on the car, we need to use the equation:
Work = Force x Distance x cos(θ)
In this case, the force applied is 1000 N (given). The distance the car covers while braking can be calculated by subtracting the initial and final positions of the car. From the data given, the initial position is not explicitly mentioned, but we know the car slows down from 108 km/h to 90 km/h over the course of 4 s.
First, we need to convert the speeds from km/h to m/s:
Initial speed = 108 km/h = 30 m/s
Final speed = 90 km/h = 25 m/s
Next, we calculate the average speed:
Average speed = (Initial speed + Final speed) / 2 = (30 m/s + 25 m/s) / 2 = 27.5 m/s
Using the formula, average speed = distance / time, we can solve for the distance covered during the 4 seconds:
27.5 m/s = distance / 4 s
distance = 27.5 m/s * 4 s = 110 m
Since the distance covered is given as 0.1 km, we need to convert it to meters:
Distance = 0.1 km = 100 m
Now we can calculate the work done by the brakes:
Work = Force x Distance x cos(θ)
= 1000 N * 100 m * cos(180°) [since the force and displacement are opposite directions]
Cosine of 180° is -1, so the equation becomes:
Work = 1000 N * 100 m * -1 = -100,000 J
Therefore, the work done by the brakes on the car is -100,000 Joules. Note that the negative sign indicates that the work is done against the motion of the car, which is expected since the car is slowing down.
d = 0.1km = 100 m.
Work = F*d = 1000*100 = ___ Joules.
So given that the answers are
a) none of the above
b) -4000 N
c) 4000 N
d) 110 000 N
e) -110 000N
it will be a?