A car travelling at a speed of30km/h is bought to rest in a distance of 8m by applying brakes. If the same car is moving at a speed of 60km/h the in it can be brought to rest with same brakes in???
everything after "60 km/h" is just gibberish.
Assuming that you mean:
"A car travelling at a speed of 30km/h is bought to rest in a distance of 8m by applying brakes. If the same car is moving at a speed of 60km/h, then the distance in which it can be brought to rest with the same brakes is?"
In the initial case,
v = 0
u = 30km/hr = 8.33m/s
s = 8m
Using 2as = v^2 - u^2,
a = - (8.33^2/2*8)
= -69.444/16
= -4.34
Hence, this car's brakes always provide a deceleration of -4.34m/s^2
Coming to the second case,
a = -4.34m/s^2
v = 0
u = 60km/hr = 16.66m/s
Using the same identity,
s = -u^2/2*a
= -277.666/8.68
= 31.91m
= 32m
You could also directly say using the same equation that the stopping distance varies with the square of the initial speed, and hence when the initial speed is doubled, the stopping distance is four times as much.
Arora's last statement about the relation of distance related to the square of the speed is the point of this conceptual question. Variants of this question often appear in college advanced placement exams. Double speed, distance to stop doubles^2 (quadruples).
To find out the distance required to bring the car to rest when it is moving at a speed of 60 km/h, we can use the concept of kinetic energy.
When a car is brought to rest, the initial kinetic energy of the car is equal to the work done by the brakes to stop the car.
The kinetic energy (KE) of an object can be calculated using the formula:
KE = (1/2) * mass * velocity^2
Since the mass of the car is not given, we can disregard it for our calculations, as it cancels out in this scenario.
So, let's calculate the initial kinetic energy of the car when it is moving at 30 km/h:
KE1 = (1/2) * velocity1^2
= (1/2) * (30 km/h)^2
Next, we can calculate the distance required to bring the car to rest at 30 km/h using the formula:
KE1 = work done by brake = force * distance
Since the force applied remains the same, we can write:
distance1 = KE1 / force
Similarly, for the car moving at 60 km/h, let's calculate the distance required to bring it to rest:
KE2 = (1/2) * velocity2^2
= (1/2) * (60 km/h)^2
distance2 = KE2 / force
Since the same brakes are used to stop the car in both cases, the force applied remains constant. Therefore, distance2 will equal distance1.
So, the car moving at a speed of 60 km/h can be brought to rest in the same distance of 8 meters by applying the same brakes.