A car of mass 1000 kg moving with a velocity of 30m/s applies break and stop after 3s. Find the magnitude of retarding force, the distance travelled by the car before it came to rest and the work done by the breaking force.
a. V = Vo + a*t.
9 = 30 + a*3, a = -10 m/s^2.
F = M*a. The retarding force will be negative.
b. V^2 = Vo^2 + 2a*d.
0 = 30^2 -20d, d = ?.
c. Work = F*d in Joules.
To find the magnitude of the retarding force, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
Force = mass x acceleration.
In this case, the acceleration is the deceleration of the car, which can be calculated using the formula:
Acceleration = change in velocity / time taken.
Given that the car's initial velocity (u) is 30 m/s, final velocity (v) is 0 m/s, and the time taken (t) is 3 s, we can calculate the acceleration:
Acceleration = (v - u) / t = (0 - 30) / 3 = -10 m/s^2.
Since the acceleration is negative, it indicates that the car is decelerating or slowing down. Now, we can use the formula for force:
Force = mass x acceleration = 1000 kg x (-10 m/s^2) = -10,000 N.
The magnitude of the retarding force is 10,000 N.
To find the distance traveled by the car before it came to rest, we can use the equation of motion:
Distance = (initial velocity x time) + (1/2 x acceleration x time²).
Given that the initial velocity (u) is 30 m/s, the time taken (t) is 3 s, and the acceleration (a) is -10 m/s^2, we can calculate the distance:
Distance = (30 x 3) + (1/2 x -10 x 3²)
= 90 - 45
= 45 m.
The car traveled a distance of 45 meters before it came to rest.
To find the work done by the braking force, we can use the equation:
Work done = force x distance.
Given that the force is -10,000 N and the distance is 45 m, we can calculate the work done:
Work done = -10,000 N x 45 m
= -450,000 J.
The work done by the braking force is -450,000 Joules (J). Note that the negative sign indicates that work is done against the motion of the car.