I have NO idea how to do this! any help is great!
A car with a mass of 1330kg is traveling at 28m/s. The driver applies the brakes to bring the car to a rest over a distance of 79m. Calculate the retarding force acting on the car.
From this i can see that it gives me the
Mass:1330kg
the inicial velocity: 28m/s
and the distance: 79m
i'm trying to find the force, but i can't think of a formula using the known variables!!
you can find the force doen through W=Fd, where W is work done,F is force applied, and D is the displacement(79m)
Work done also equlals change in kinetic energy, which is -521360J, sp the force applied is -6599.5 N.
... we havn't even learned about Kinetic energy yet... my teacher must be losing it.... haha
You have to use three formulas for this one, I'm afraid.
First you need to find out how long it takes for the car to decelerate during those 79m.
Then you have to figure the acceleration, knowing the speed and the time.
And finally you have to translate that acceleration into a force.
For the first part you'll need this formula (to find out the time taken to stop):
Distance = (Final Speed + Initial Speed ) x Time/2
79 = 28 x T/2
T = 5.64s
For the second step, you have the following formula (to find the acceleration):
Final Speed = Initial Speed - Acceleration x Time
0 = 28 - A x 5.64
A = 4.96m/s^2
Finally, you have the force formula:
Force = Mass x Acceleration
F = 1330 x 4.96
Force = 6596.8N
To calculate the retarding force acting on the car, you can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):
F = m * a
In this case, the acceleration can be calculated using the following equation, which relates distance (d) and initial velocity (v) to acceleration (a):
a = (v^2 - u^2) / (2 * d)
where "v" is the final velocity (0 in this case, since the car comes to rest), "u" is the initial velocity (28 m/s in this case), and "d" is the distance (79 m).
Plugging in the given values into the equation:
v = 0 m/s
u = 28 m/s
d = 79 m
a = (0^2 - 28^2) / (2 * 79)
a = (-784) / 158
a = -4.96 m/s^2 (note the negative sign indicates deceleration)
Now, substitute the value of acceleration (a) into the formula for force (F):
F = m * a
F = 1330 kg * (-4.96 m/s^2)
Calculating this expression will give you the retarding force acting on the car.