a car of mass 100kg travering at 36km/h is brought to rest over a distance of 40m.calculate(a)accelaration(b)the average abreaking force
a. Vo = 36000m/3600s. = 10 m/s.
a = -(Vo^2)/2d = -(10^2)/80 = -1.25 m/s^2.
b. F = M*a = 100 * (-1.25) = -125 N.
The negative sign means the force opposes the motion.
A car of mass 100kg travelling 36kg/hr is brought to rest over a distance 40m. a) the acceleration of the car
To calculate the acceleration of the car, we can use the equation:
acceleration = change in velocity / time
First, let's convert the initial velocity from km/h to m/s:
36 km/h = 36 * (1000 m / 1 km) / (3600 s / 1 h) = 10 m/s
The final velocity is 0 m/s since the car comes to rest.
Now we can calculate the change in velocity:
change in velocity = final velocity - initial velocity
= 0 m/s - 10 m/s
= -10 m/s
Next, we need to find the time it takes for the car to come to rest. We can use the equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Since the final velocity is 0 m/s, the equation becomes:
0 = 10 m/s + a * t
We have the value for initial velocity (10 m/s), and we can rearrange the equation to solve for time:
10 m/s = -a * t
t = -10 m/s / a
Since we know the distance traveled (40 m) and average velocity (10 m/s), we can also use the equation:
distance = average velocity * time
40m = 10m/s * t
t = 40m / 10m/s
t = 4 s
Now, let's substitute this value of time into the equation we found earlier:
4s = -10 m/s / a
a = -10 m/s / 4 s
a = -2.5 m/s^2
Therefore, the acceleration of the car is -2.5 m/s^2 (negative indicating deceleration).
To calculate the average braking force, we can use the equation:
force = mass * acceleration
Given the mass of the car is 100 kg and the acceleration calculated is -2.5 m/s^2, we can substitute the values:
force = 100 kg * (-2.5 m/s^2)
force = -250 N
Therefore, the average braking force is -250 N (negative indicating opposite direction to motion).
To calculate the acceleration and the average braking force, we can use the equations of motion.
(a) Acceleration (a):
Acceleration can be calculated using the equation:
a = (vf - vi) / t,
where:
- vf is the final velocity (0 since the car comes to rest),
- vi is the initial velocity,
- t is the time taken to bring the car to rest.
First, we need to convert the initial velocity from km/h to m/s:
vi = 36 km/h = (36 * 1000) m / (60 * 60) s = 10 m/s.
Since the car comes to rest, final velocity (vf) is 0 m/s.
Now, we need to calculate the time it takes (t) to bring the car to rest. To do this, we can use the kinematic equation:
vf^2 = vi^2 + 2ad,
where:
- vf is the final velocity (0 m/s),
- vi is the initial velocity (10 m/s),
- a is the acceleration (which we are trying to calculate),
- d is the distance traveled (40 m).
Rearranging the equation:
0 = 10^2 + 2a * 40,
0 = 100 + 80a.
Solving for a:
80a = -100,
a = -100 / 80 = -1.25 m/s^2.
So, the acceleration of the car is -1.25 m/s^2.
(b) Average braking force (F):
The average braking force can be calculated using Newton's second law:
F = m * a,
where:
- F is the average braking force (which we are trying to calculate),
- m is the mass of the car (100 kg),
- a is the acceleration (-1.25 m/s^2).
Substituting the values:
F = 100 kg * (-1.25 m/s^2) = -125 N.
Note: The negative sign indicates that the force is directed opposite to the motion of the car.
So, the average braking force exerted on the car is 125 N.